236:@0.052592:0.966074:0.080768:0.966074:0.080768:0.949450:0.052592:0.949450:0.000000:0.000000:0.000000
Tema 6:@0.124729:0.083964:0.219414:0.083964:0.219414:0.055923:0.124729:0.055923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Variaciones, combinaciones  :@0.305293:0.069842:0.677937:0.069842:0.677937:0.042186:0.305293:0.042186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y permutaciones:@0.305293:0.096253:0.522826:0.096253:0.522826:0.068597:0.305293:0.068597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En el concurso de declamación de una institución educativa se han presentado 12 :@0.304744:0.226002:0.907071:0.226002:0.907071:0.210333:0.304744:0.210333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
participantes, de los cuales tres serán premiados, uno será el ganador, otro ocupará :@0.304744:0.242599:0.907121:0.242599:0.907121:0.226929:0.304744:0.226929:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el segundo lugar y se acreditará el tercer lugar. ¿De cuántas maneras se puede :@0.304744:0.259195:0.907047:0.259195:0.907047:0.243525:0.304744:0.243525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
formar ese cuadro de premiados?:@0.304744:0.275791:0.550215:0.275791:0.550215:0.260122:0.304744:0.260122:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Observamos que existe un conjunto de participantes, conformado por 12 elementos; :@0.304744:0.299510:0.907176:0.299510:0.907176:0.283841:0.304744:0.283841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de ellos solo tres serán seleccionados para ser premiados con cierto orden, de :@0.304744:0.316107:0.907029:0.316107:0.907029:0.300437:0.304744:0.300437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
acuerdo con su desenvolvimiento. Las características de esta situación corresponden :@0.304744:0.332703:0.907125:0.332703:0.907125:0.317033:0.304744:0.317033:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a una variación ordinaria; por lo tanto, definamos este parámetro matemático.:@0.304744:0.349300:0.860577:0.349300:0.860577:0.333630:0.304744:0.333630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Se denominan variaciones ordinarias de :@0.319266:0.377956:0.633974:0.377956:0.633974:0.362286:0.319266:0.362286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.638580:0.377956:0.653212:0.377956:0.653212:0.361595:0.638580:0.361595:0.000000
 elementos tomados de   en :@0.653212:0.377956:0.891242:0.377956:0.891242:0.362286:0.653212:0.362286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.850240:0.377956:0.859749:0.377956:0.859749:0.361595:0.850240:0.361595:0.000000
 :@0.887169:0.377956:0.891205:0.377956:0.891205:0.362286:0.887169:0.362286:0.000000
n m n:@0.315913:0.394552:0.375360:0.394552:0.375360:0.378191:0.315913:0.378191:0.000000:0.000000:0.000000:0.000000:0.000000
 ( ≥ ) a los distintos grupos formados por n elementos, en donde se cumple :@0.325421:0.394552:0.894559:0.394552:0.894559:0.378883:0.325421:0.378883:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
   :@0.348371:0.394552:0.366423:0.394552:0.366423:0.377652:0.348371:0.377652:0.000000:0.000000:0.000000
que: no entran todos los elementos, importa el orden y no hay repetición de :@0.315913:0.411149:0.894577:0.411149:0.894577:0.395479:0.315913:0.395479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
elementos. Para calcularlas usamos la fórmula::@0.315913:0.427745:0.652746:0.427745:0.652746:0.412075:0.315913:0.412075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
V:@0.547628:0.467000:0.561924:0.467000:0.568925:0.443116:0.554629:0.443116:0.000000
m:@0.612509:0.452028:0.627845:0.452028:0.632512:0.436105:0.617176:0.436105:0.000000
mn:@0.600434:0.471791:0.640056:0.471791:0.644723:0.455869:0.605101:0.455869:0.000000:0.000000
!:@0.630615:0.452028:0.634491:0.452028:0.634491:0.436105:0.630615:0.436105:0.000000
(:@0.596463:0.471791:0.601425:0.471791:0.601425:0.455869:0.596463:0.455869:0.000000
)!:@0.642639:0.471791:0.651889:0.471791:0.651889:0.455869:0.642639:0.455869:0.000000:0.000000
m:@0.569376:0.464285:0.578263:0.464285:0.580968:0.455058:0.572081:0.455058:0.000000
n:@0.569371:0.451270:0.575188:0.451270:0.577893:0.442043:0.572076:0.442043:0.000000
=:@0.582527:0.461380:0.592807:0.461380:0.592807:0.445556:0.582527:0.445556:0.000000
−:@0.619764:0.472480:0.630044:0.472480:0.630044:0.456656:0.619764:0.456656:0.000000
Apliquemos la fórmula a nuestra situación:@0.304744:0.513130:0.613110:0.513130:0.613110:0.497460:0.304744:0.497460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.336992:0.546332:0.347109:0.546332:0.347109:0.530760:0.336992:0.530760:0.000000
−:@0.376151:0.556823:0.386268:0.556823:0.386268:0.541250:0.376151:0.541250:0.000000
=:@0.411383:0.546332:0.421500:0.546332:0.421500:0.530760:0.411383:0.530760:0.000000
×:@0.441070:0.537370:0.451186:0.537370:0.451186:0.521798:0.441070:0.521798:0.000000
×:@0.470222:0.537370:0.480339:0.537370:0.480339:0.521798:0.470222:0.521798:0.000000
×:@0.502471:0.537370:0.512587:0.537370:0.512587:0.521798:0.502471:0.521798:0.000000
=:@0.533208:0.546332:0.543325:0.546332:0.543325:0.530760:0.533208:0.530760:0.000000
×:@0.565622:0.546332:0.575739:0.546332:0.575739:0.530760:0.565622:0.530760:0.000000
×:@0.594775:0.546332:0.604891:0.546332:0.604891:0.530760:0.594775:0.530760:0.000000
=:@0.627539:0.546332:0.637656:0.546332:0.637656:0.530760:0.627539:0.530760:0.000000
V:@0.305791:0.551431:0.319473:0.551431:0.319473:0.526889:0.305791:0.526889:0.000000
12!:@0.367932:0.536697:0.390064:0.536697:0.390064:0.521027:0.367932:0.521027:0.000000:0.000000:0.000000
(123)!:@0.351439:0.556142:0.407238:0.556142:0.407238:0.540472:0.351439:0.540472:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
12 11 10 9!:@0.420912:0.536697:0.529045:0.536697:0.529045:0.521027:0.420912:0.521027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
9!:@0.468694:0.556142:0.482405:0.556142:0.482405:0.540472:0.468694:0.540472:0.000000:0.000000
12 11 10 1320:@0.545445:0.545645:0.677977:0.545645:0.677977:0.529975:0.545445:0.529975:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
12:@0.323433:0.549034:0.333717:0.549034:0.333717:0.539953:0.323433:0.539953:0.000000:0.000000
3:@0.324116:0.536226:0.329328:0.536226:0.329328:0.527144:0.324116:0.527144:0.000000
El cuadro de premiados puede formarse de 1 320 distintas formas.:@0.304744:0.584466:0.788114:0.584466:0.788114:0.568797:0.304744:0.568797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 1:@0.304744:0.602804:0.374249:0.602804:0.374249:0.587691:0.304744:0.587691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuántos números de tres cifras diferentes se pueden formar con los dígitos: 0, 1, :@0.304744:0.626842:0.907069:0.626842:0.907069:0.611173:0.304744:0.611173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3, 5, 7 y 9? :@0.304744:0.643439:0.382435:0.643439:0.382435:0.627769:0.304744:0.627769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Solución:@0.304744:0.661777:0.365404:0.661777:0.365404:0.646664:0.304744:0.646664:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
De los seis elementos con los que se dispone, debemos tomar tres. Importa el :@0.304744:0.685815:0.907031:0.685815:0.907031:0.670145:0.304744:0.670145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
orden y las cifras deben ser distintas, por lo tanto, se trata de una variación. Sin em-:@0.304744:0.702411:0.903163:0.702411:0.903163:0.686742:0.304744:0.686742:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
bargo, como ningún número empieza con cero, tenemos que separar el número :@0.304744:0.719008:0.907051:0.719008:0.907051:0.703338:0.304744:0.703338:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en dos bloques: el primer bloque lo pueden ocupar solo 1, 3, 5, 7 y 9. Ahí tenemos :@0.304744:0.735604:0.906994:0.735604:0.906994:0.719934:0.304744:0.719934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
una variación donde   = 5 y  = 1. :@0.304744:0.752200:0.562712:0.752200:0.562712:0.736531:0.304744:0.736531:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.459775:0.752200:0.474407:0.752200:0.474407:0.735839:0.459775:0.735839:0.000000
n :@0.518633:0.752200:0.531459:0.752200:0.531459:0.735839:0.518633:0.735839:0.000000:0.000000
El segundo bloque, de dos números, lo puede ocupar cualquier dígito, menos el :@0.304744:0.775919:0.907103:0.775919:0.907103:0.760250:0.304744:0.760250:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inicial, resultando una variación, en la que   = 5 y   = 2.:@0.304744:0.792516:0.713301:0.792516:0.713301:0.776846:0.304744:0.776846:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.613681:0.792516:0.628313:0.792516:0.628313:0.776155:0.613681:0.776155:0.000000
n:@0.672539:0.792516:0.682048:0.792516:0.682048:0.776155:0.672539:0.776155:0.000000
La variación total se calcula como el producto de las dos variaciones::@0.304744:0.816235:0.806560:0.816235:0.806560:0.800565:0.304744:0.800565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.323433:0.855564:0.338608:0.855564:0.338608:0.832204:0.323433:0.832204:0.000000
⋅:@0.363481:0.849449:0.368088:0.849449:0.368088:0.833876:0.363481:0.833876:0.000000
=:@0.394679:0.849449:0.404796:0.849449:0.404796:0.833876:0.394679:0.833876:0.000000
−:@0.425780:0.859940:0.435897:0.859940:0.435897:0.844367:0.425780:0.844367:0.000000
⋅:@0.456247:0.849449:0.460854:0.849449:0.460854:0.833876:0.456247:0.833876:0.000000
−:@0.479910:0.859940:0.490027:0.859940:0.490027:0.844367:0.479910:0.844367:0.000000
=:@0.515563:0.849449:0.525679:0.849449:0.525679:0.833876:0.515563:0.833876:0.000000
×:@0.541380:0.840487:0.551496:0.840487:0.551496:0.824914:0.541380:0.824914:0.000000
⋅:@0.571896:0.849449:0.576503:0.849449:0.576503:0.833876:0.571896:0.833876:0.000000
××:@0.590268:0.840487:0.626092:0.840487:0.626092:0.824914:0.590268:0.824914:0.000000:0.000000
=×:@0.645920:0.849449:0.680379:0.849449:0.680379:0.833876:0.645920:0.833876:0.000000:0.000000
=:@0.704188:0.849449:0.714305:0.849449:0.714305:0.833876:0.704188:0.833876:0.000000
VV V:@0.305791:0.854547:0.381561:0.854547:0.381561:0.830005:0.305791:0.830005:0.000000:0.000000:0.000000:0.000000
5!:@0.425046:0.839813:0.437964:0.839813:0.437964:0.824143:0.425046:0.824143:0.000000:0.000000
(5 1)! (5 2)!:@0.409125:0.859258:0.511398:0.859258:0.511398:0.843589:0.409125:0.843589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5!:@0.481103:0.839813:0.494021:0.839813:0.494021:0.824143:0.481103:0.824143:0.000000:0.000000
54! 54 3!:@0.530415:0.839813:0.641755:0.839813:0.641755:0.824143:0.530415:0.824143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4!:@0.543075:0.859258:0.557154:0.859258:0.557154:0.843589:0.543075:0.843589:0.000000:0.000000
3!:@0.604070:0.859258:0.616988:0.859258:0.616988:0.843589:0.604070:0.843589:0.000000:0.000000
520 100:@0.659298:0.848761:0.742996:0.848761:0.742996:0.833091:0.659298:0.833091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.356519:0.852151:0.361730:0.852151:0.361730:0.843069:0.356519:0.843069:0.000000
1:@0.355835:0.839342:0.361047:0.839342:0.361047:0.830261:0.355835:0.830261:0.000000
5:@0.386197:0.852151:0.391409:0.852151:0.391409:0.843069:0.386197:0.843069:0.000000
2:@0.386197:0.839342:0.391409:0.839342:0.391409:0.830261:0.386197:0.830261:0.000000
Existen otras formas de disponer los elementos de un conjunto.:@0.304744:0.884020:0.769960:0.884020:0.769960:0.868350:0.304744:0.868350:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El factorial de un :@0.105654:0.561685:0.220155:0.561685:0.220155:0.547440:0.105654:0.547440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
número es el producto :@0.105654:0.576773:0.262336:0.576773:0.262336:0.562528:0.105654:0.562528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de los “ ” factores :@0.105654:0.591861:0.224395:0.591861:0.224395:0.577615:0.105654:0.577615:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.152377:0.591861:0.161021:0.591861:0.161021:0.576987:0.152377:0.576987:0.000000
consecutivos desde “n” :@0.105654:0.606948:0.259456:0.606948:0.259456:0.592703:0.105654:0.592703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
hasta 1. El :@0.105654:0.622036:0.174724:0.622036:0.174724:0.607791:0.105654:0.607791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
factorial de :@0.174724:0.622036:0.259961:0.622036:0.259961:0.606672:0.174724:0.606672:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un número:@0.105654:0.637123:0.185461:0.637123:0.185461:0.621759:0.105654:0.621759:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 se denota :@0.185461:0.637123:0.258753:0.637123:0.258753:0.622878:0.185461:0.622878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por :@0.105654:0.652211:0.132425:0.652211:0.132425:0.637966:0.105654:0.637966:0.000000:0.000000:0.000000:0.000000
n!:@0.132425:0.652211:0.146212:0.652211:0.146212:0.636847:0.132425:0.636847:0.000000:0.000000
=:@0.123111:0.675001:0.132975:0.675001:0.132975:0.659817:0.123111:0.659817:0.000000
−:@0.162423:0.675001:0.172286:0.675001:0.172286:0.659817:0.162423:0.659817:0.000000
−:@0.202328:0.675001:0.212192:0.675001:0.212192:0.659817:0.202328:0.659817:0.000000
−:@0.246024:0.675001:0.255887:0.675001:0.255887:0.659817:0.246024:0.659817:0.000000
⋅⋅:@0.290725:0.675001:0.311351:0.675001:0.311351:0.659817:0.290725:0.659817:0.000000:0.000000
nn:@0.136533:0.674340:0.160249:0.674340:0.160249:0.658388:0.136533:0.658388:0.000000:0.000000
n:@0.190901:0.674340:0.200172:0.674340:0.200172:0.658388:0.190901:0.658388:0.000000
n:@0.234597:0.674340:0.243867:0.674340:0.243867:0.658388:0.234597:0.658388:0.000000
n!:@0.107445:0.674340:0.120507:0.674340:0.120507:0.659062:0.107445:0.659062:0.000000:0.000000
(:@0.145067:0.674340:0.149829:0.674340:0.149829:0.659062:0.145067:0.659062:0.000000
1)(:@0.173850:0.674340:0.189751:0.674340:0.189751:0.659062:0.173850:0.659062:0.000000:0.000000:0.000000
2)(:@0.214905:0.674340:0.233447:0.674340:0.233447:0.659062:0.214905:0.659062:0.000000:0.000000:0.000000
3)...3 21`:@0.258600:0.674340:0.323246:0.674340:0.323246:0.659062:0.258600:0.659062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
−:@-0.003105:0.697765:0.006759:0.697765:0.006759:0.682582:-0.003105:0.682582:0.000000
−:@0.036799:0.697765:0.046663:0.697765:0.046663:0.682582:0.036799:0.682582:0.000000
−:@0.080495:0.697765:0.090359:0.697765:0.090359:0.682582:0.080495:0.682582:0.000000
⋅⋅:@0.125207:0.697765:0.145833:0.697765:0.145833:0.682582:0.125207:0.682582:0.000000:0.000000
n:@0.025375:0.697104:0.034646:0.697104:0.034646:0.681152:0.025375:0.681152:0.000000
n:@0.069071:0.697104:0.078342:0.697104:0.078342:0.681152:0.069071:0.681152:0.000000
1)(:@0.008324:0.697104:0.024225:0.697104:0.024225:0.681827:0.008324:0.681827:0.000000:0.000000:0.000000
2)(:@0.049379:0.697104:0.067921:0.697104:0.067921:0.681827:0.049379:0.681827:0.000000:0.000000:0.000000
3)...3 21`:@0.093074:0.697104:0.157720:0.697104:0.157720:0.681827:0.093074:0.681827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por ejemplo::@0.105654:0.723354:0.189332:0.723354:0.189332:0.709109:0.105654:0.709109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=× ×× ×× =:@0.125024:0.746561:0.279116:0.746561:0.279116:0.730989:0.125024:0.730989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6! 65 43 21 720:@0.108642:0.745884:0.308563:0.745884:0.308563:0.730214:0.108642:0.730214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=× ×× ×× =:@-0.037404:0.765191:0.116688:0.765191:0.116688:0.749618:-0.037404:0.749618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
6! 65 43 21 720:@-0.053786:0.764513:0.146136:0.764513:0.146136:0.748843:-0.053786:0.748843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
0! = 1:@0.105654:0.789956:0.142794:0.789956:0.142794:0.775711:0.105654:0.775711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recuerda que...:@0.135707:0.536659:0.257788:0.536659:0.257788:0.519758:0.135707:0.519758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuáles son los números que puedes formar con los números 3, 6 y 9 sin repetir :@0.311168:0.166194:0.900694:0.166194:0.900694:0.150524:0.311168:0.150524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cifras? :@0.311168:0.182790:0.359799:0.182790:0.359799:0.167120:0.311168:0.167120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.344861:0.139565:0.470369:0.139565:0.470369:0.122665:0.344861:0.122665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock, 1678448540.:@0.092073:0.360866:0.092073:0.281905:0.080685:0.281905:0.080685:0.360866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.3.10.:@0.096359:0.927843:0.142269:0.927843:0.142269:0.917089:0.096359:0.917089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Aplicar métodos de conteo (combinaciones y permutaciones) en el cálculo de probabilidades.:@0.142269:0.927843:0.583877:0.927843:0.583877:0.917872:0.142269:0.917872:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.4.3.11.:@0.096359:0.937903:0.142269:0.937903:0.142269:0.927148:0.096359:0.927148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 Calcular el factorial de un número natural y el coeficiente binomial en el cálculo de probabilidades.:@0.142269:0.937903:0.604294:0.937903:0.604294:0.927932:0.142269:0.927932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
369 – 396 – 639 – 693 – 936 y 963:@0.408195:0.180665:0.565497:0.180665:0.565497:0.170693:0.408195:0.170693:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000