122:@0.048054:0.510692:0.076414:0.510692:0.076414:0.494068:0.048054:0.494068:0.000000:0.000000:0.000000 Tema:@0.047190:0.135475:0.083321:0.135475:0.083321:0.113749:0.047190:0.113749:0.000000:0.000000:0.000000:0.000000 d) :@0.532224:0.740665:0.552292:0.740665:0.552292:0.723764:0.532224:0.723764:0.000000:0.000000:0.000000 (15 – 9)! :@0.565466:0.731651:0.631382:0.731651:0.631382:0.715262:0.565466:0.715262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (6 – 2)!:@0.565466:0.750308:0.622389:0.750308:0.622389:0.733919:0.565466:0.733919:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.642181:0.740668:0.646216:0.740668:0.646216:0.724280:0.642181:0.724280:0.000000 e) :@0.532223:0.816002:0.551093:0.816002:0.551093:0.799102:0.532223:0.799102:0.000000:0.000000:0.000000 8:@0.575426:0.807298:0.584418:0.807298:0.584418:0.790909:0.575426:0.790909:0.000000 4:@0.575426:0.824696:0.584418:0.824696:0.584418:0.808307:0.575426:0.808307:0.000000 :@0.594369:0.815997:0.598405:0.815997:0.598405:0.799608:0.594369:0.799608:0.000000 f) :@0.532213:0.896642:0.549037:0.896642:0.549037:0.879741:0.532213:0.879741:0.000000:0.000000:0.000000 10:@0.576022:0.887073:0.586507:0.887073:0.586507:0.877518:0.576022:0.877518:0.000000:0.000000 C:@0.565466:0.895899:0.575380:0.895899:0.575380:0.879537:0.565466:0.879537:0.000000 5:@0.575380:0.899062:0.580623:0.899062:0.580623:0.889508:0.575380:0.889508:0.000000 El coeficiente binomial corresponde al número de formas en que se :@0.376903:0.223390:0.883938:0.223390:0.883938:0.207001:0.376903:0.207001:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 puede extraer subconjuntos de tamaño a partir de un conjunto de :@0.376903:0.239986:0.883903:0.239986:0.883903:0.223597:0.376903:0.223597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.673201:0.239986:0.682710:0.239986:0.682710:0.223625:0.673201:0.223625:0.000000 m:@0.376903:0.256582:0.391535:0.256582:0.391535:0.240221:0.376903:0.240221:0.000000 elementos distintos. En la siguiente sección veremos que el coefi-:@0.391535:0.256582:0.879941:0.256582:0.879941:0.240194:0.391535:0.240194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ciente binomial recibe el nombre de combinaciones de en ::@0.376903:0.273179:0.841921:0.273179:0.841921:0.256790:0.376903:0.256790:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.787688:0.273179:0.797197:0.273179:0.797197:0.256818:0.787688:0.256818:0.000000 m:@0.824083:0.273179:0.838714:0.273179:0.838714:0.256818:0.824083:0.256818:0.000000 El coeficiente binomial se representa como: :@0.376903:0.293343:0.699954:0.293343:0.699954:0.276954:0.376903:0.276954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.572382:0.312316:0.587013:0.312316:0.587013:0.295955:0.572382:0.295955:0.000000 n:@0.574943:0.329715:0.584452:0.329715:0.584452:0.313353:0.574943:0.313353:0.000000 = :@0.598383:0.321126:0.613402:0.321126:0.613402:0.304737:0.598383:0.304737:0.000000:0.000000 mCn = C:@0.613402:0.321126:0.674987:0.321126:0.674987:0.304765:0.613402:0.304765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.674980:0.313813:0.685444:0.313813:0.685444:0.304274:0.674980:0.304274:0.000000:0.000000 n:@0.676076:0.320787:0.681619:0.320787:0.681619:0.311249:0.676076:0.311249:0.000000 y se lo calcula mediante la expresión: :@0.376903:0.365345:0.651287:0.365345:0.651287:0.348956:0.376903:0.348956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.658424:0.355074:0.673055:0.355074:0.673055:0.338713:0.658424:0.338713:0.000000 n:@0.660985:0.372473:0.670494:0.372473:0.670494:0.356112:0.660985:0.356112:0.000000 = :@0.684425:0.364092:0.699444:0.364092:0.699444:0.347703:0.684425:0.347703:0.000000:0.000000 ! :@0.699033:0.355074:0.773978:0.355074:0.773978:0.338685:0.699033:0.338685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.727283:0.355074:0.741914:0.355074:0.741914:0.338713:0.727283:0.338713:0.000000 ( – )! !:@0.699033:0.373731:0.767363:0.373731:0.767363:0.357343:0.699033:0.357343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m n n:@0.703916:0.373731:0.763548:0.373731:0.763548:0.357370:0.703916:0.357370:0.000000:0.000000:0.000000:0.000000:0.000000 Para saber :@0.225828:0.250066:0.297394:0.250066:0.297394:0.235167:0.225828:0.235167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 más acerca :@0.225828:0.265153:0.303775:0.265153:0.303775:0.250254:0.225828:0.250254:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 del coeficiente :@0.225828:0.280241:0.327849:0.280241:0.327849:0.265342:0.225828:0.265342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 binomial, :@0.225828:0.295329:0.291246:0.295329:0.291246:0.280430:0.225828:0.280430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 mira:@0.291246:0.295329:0.322607:0.295329:0.322607:0.280216:0.291246:0.280216:0.000000:0.000000:0.000000:0.000000 el :@0.322607:0.295329:0.341621:0.295329:0.341621:0.280430:0.322607:0.280430:0.000000:0.000000:0.000000:0.000000 video del enlace::@0.225828:0.310416:0.337952:0.310416:0.337952:0.295517:0.225828:0.295517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 TIC:@0.165439:0.230633:0.185408:0.230633:0.185408:0.208907:0.165439:0.208907:0.000000:0.000000:0.000000 mayedu.ec/ctm9/p122:@0.160720:0.335032:0.312143:0.335032:0.312143:0.319906:0.160720:0.319906:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. :@0.114617:0.684902:0.133358:0.684902:0.133358:0.667766:0.114617:0.667766:0.000000:0.000000:0.000000 Halla :@0.147861:0.684902:0.190244:0.684902:0.190244:0.668278:0.147861:0.668278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el resultado de las siguientes expresiones.:@0.190244:0.684902:0.494995:0.684902:0.494995:0.668513:0.190244:0.668513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.114617:0.709631:0.118339:0.709631:0.118339:0.692495:0.114617:0.692495:0.000000 a) :@0.147861:0.738910:0.166583:0.738910:0.166583:0.722009:0.147861:0.722009:0.000000:0.000000:0.000000 6! :@0.181099:0.729900:0.201978:0.729900:0.201978:0.713511:0.181099:0.713511:0.000000:0.000000:0.000000:0.000000 2!:@0.181099:0.748557:0.197942:0.748557:0.197942:0.732168:0.181099:0.732168:0.000000:0.000000:0.000000 :@0.204834:0.738917:0.208870:0.738917:0.208870:0.722528:0.204834:0.722528:0.000000 b) :@0.147856:0.818580:0.167887:0.818580:0.167887:0.801679:0.147856:0.801679:0.000000:0.000000:0.000000 9! :@0.181099:0.809560:0.201978:0.809560:0.201978:0.793171:0.181099:0.793171:0.000000:0.000000:0.000000:0.000000 5!:@0.181099:0.828217:0.197942:0.828217:0.197942:0.811828:0.181099:0.811828:0.000000:0.000000:0.000000 :@0.204834:0.818577:0.208870:0.818577:0.208870:0.802188:0.204834:0.802188:0.000000 c) :@0.147856:0.896981:0.165491:0.896981:0.165491:0.880081:0.147856:0.880081:0.000000:0.000000:0.000000 10! :@0.181099:0.887963:0.251327:0.887963:0.251327:0.871574:0.181099:0.871574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (12 – 3)!:@0.181099:0.906620:0.247015:0.906620:0.247015:0.890231:0.181099:0.890231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.257814:0.896980:0.261849:0.896980:0.261849:0.880591:0.257814:0.880591:0.000000 Factorial de un número. :@0.115202:0.167763:0.312118:0.167763:0.312118:0.150862:0.115202:0.150862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El factorial de un número entero positivo se define como el producto de :@0.313795:0.167763:0.883964:0.167763:0.883964:0.151374:0.313795:0.151374:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.629534:0.167763:0.639043:0.167763:0.639043:0.151402:0.629534:0.151402:0.000000 :@0.879894:0.167763:0.883929:0.167763:0.883929:0.151374:0.879894:0.151374:0.000000 todos los números enteros positivos desde 1 hasta . Se escribe !, y se lee \ factorial\. :@0.115202:0.184359:0.751061:0.184359:0.751061:0.167970:0.115202:0.167970:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.489095:0.184359:0.498604:0.184359:0.498604:0.167998:0.489095:0.167998:0.000000 n:@0.584051:0.184359:0.593560:0.184359:0.593560:0.167998:0.584051:0.167998:0.000000 n:@0.667970:0.184359:0.677479:0.184359:0.677479:0.167998:0.667970:0.167998:0.000000 Por ejemplo: 3! = 3 . 2 . 1. :@0.115202:0.204524:0.301450:0.204524:0.301450:0.188135:0.115202:0.188135:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Factorial de un número y coeficiente binomial:@0.115891:0.141978:0.785618:0.141978:0.785618:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Calcular el factorial de un número natural y el coeficiente binomial. (Ref. M.4.3.11.):@0.125388:0.074999:0.504681:0.074999:0.504681:0.064570:0.125388:0.064570:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 6:@0.054104:0.122645:0.076408:0.122645:0.076408:0.065614:0.054104:0.065614:0.000000 Taller:@0.174831:0.643997:0.235725:0.643997:0.235725:0.610050:0.174831:0.610050:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Calcula del factorial de un número y el coeficiente binomial. (Ref. I.M.4.8.2.):@0.255852:0.632023:0.601560:0.632023:0.601560:0.621593:0.255852:0.621593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Actividad resuelta:@0.115354:0.390348:0.272476:0.390348:0.272476:0.371911:0.115354:0.371911:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Tengamos:@0.115354:0.413690:0.187423:0.413690:0.187423:0.398577:0.115354:0.398577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en cuenta que 0! = 1:@0.187423:0.413690:0.328696:0.413690:0.328696:0.398791:0.187423:0.398791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. :@0.115354:0.438990:0.134095:0.438990:0.134095:0.421855:0.115354:0.421855:0.000000:0.000000:0.000000 Calcula:@0.148597:0.438990:0.204028:0.438990:0.204028:0.422366:0.148597:0.422366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las siguientes expresiones.:@0.204028:0.438990:0.400280:0.438990:0.400280:0.422601:0.204028:0.422601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a) :@0.148597:0.468269:0.167320:0.468269:0.167320:0.451369:0.148597:0.451369:0.000000:0.000000:0.000000 8! :@0.181836:0.459258:0.202715:0.459258:0.202715:0.442869:0.181836:0.442869:0.000000:0.000000:0.000000:0.000000 4!:@0.181836:0.477915:0.198679:0.477915:0.198679:0.461526:0.181836:0.461526:0.000000:0.000000:0.000000 b) :@0.340664:0.468275:0.360695:0.468275:0.360695:0.451375:0.340664:0.451375:0.000000:0.000000:0.000000 6! :@0.373906:0.459258:0.394784:0.459258:0.394784:0.442869:0.373906:0.442869:0.000000:0.000000:0.000000:0.000000 0!:@0.373906:0.477915:0.390749:0.477915:0.390749:0.461526:0.373906:0.461526:0.000000:0.000000:0.000000 c) :@0.532734:0.470226:0.550369:0.470226:0.550369:0.453325:0.532734:0.453325:0.000000:0.000000:0.000000 7:@0.575933:0.461531:0.584926:0.461531:0.584926:0.445142:0.575933:0.445142:0.000000 3:@0.575933:0.478930:0.584926:0.478930:0.584926:0.462541:0.575933:0.462541:0.000000 d) :@0.724810:0.467492:0.744878:0.467492:0.744878:0.450592:0.724810:0.450592:0.000000:0.000000:0.000000 12 10:@0.758054:0.467492:0.803938:0.467492:0.803938:0.451103:0.758054:0.451103:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.776039:0.467492:0.785953:0.467492:0.785953:0.451131:0.776039:0.451131:0.000000 Solución:@0.115371:0.500533:0.184585:0.500533:0.184585:0.483632:0.115371:0.483632:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a) :@0.148615:0.526243:0.167337:0.526243:0.167337:0.509343:0.148615:0.509343:0.000000:0.000000:0.000000 8! :@0.181836:0.517240:0.202715:0.517240:0.202715:0.500851:0.181836:0.500851:0.000000:0.000000:0.000000:0.000000 4!:@0.181836:0.535897:0.198679:0.535897:0.198679:0.519508:0.181836:0.519508:0.000000:0.000000:0.000000 = :@0.205571:0.526257:0.224625:0.526257:0.224625:0.509868:0.205571:0.509868:0.000000:0.000000:0.000000 8 7 6 5 4! :@0.224634:0.517240:0.333080:0.517240:0.333080:0.500851:0.224634:0.500851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⋅ ⋅ ⋅ ⋅ :@0.241403:0.517917:0.316403:0.517917:0.316403:0.502345:0.241403:0.502345:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4!:@0.224634:0.535897:0.281833:0.535897:0.281833:0.519508:0.224634:0.519508:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = 1 680:@0.329045:0.526257:0.388105:0.526257:0.388105:0.509868:0.329045:0.509868:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b) :@0.148601:0.572132:0.168632:0.572132:0.168632:0.555232:0.148601:0.555232:0.000000:0.000000:0.000000 6! :@0.181836:0.563117:0.202715:0.563117:0.202715:0.546729:0.181836:0.546729:0.000000:0.000000:0.000000:0.000000 0!:@0.181836:0.581775:0.198679:0.581775:0.198679:0.565386:0.181836:0.565386:0.000000:0.000000:0.000000 = :@0.205571:0.572135:0.224625:0.572135:0.224625:0.555746:0.205571:0.555746:0.000000:0.000000:0.000000 6 5 4 3 2 1 :@0.224634:0.563117:0.352909:0.563117:0.352909:0.546729:0.224634:0.546729:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⋅ ⋅ ⋅ ⋅ ⋅ :@0.241698:0.563795:0.339880:0.563795:0.339880:0.548222:0.241698:0.548222:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.224634:0.581775:0.298197:0.581775:0.298197:0.565386:0.224634:0.565386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = 720:@0.361330:0.572135:0.407362:0.572135:0.407362:0.555746:0.361330:0.555746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c) :@0.502928:0.526066:0.520563:0.526066:0.520563:0.509165:0.502928:0.509165:0.000000:0.000000:0.000000 7:@0.546127:0.517362:0.555120:0.517362:0.555120:0.500973:0.546127:0.500973:0.000000 3:@0.546127:0.534760:0.555120:0.534760:0.555120:0.518371:0.546127:0.518371:0.000000 = :@0.565071:0.526061:0.584125:0.526061:0.584125:0.509672:0.565071:0.509672:0.000000:0.000000:0.000000 7! :@0.584133:0.517042:0.665547:0.517042:0.665547:0.500653:0.584133:0.500653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (7 – 3)! 3!:@0.584133:0.537207:0.659042:0.537207:0.659042:0.520818:0.584133:0.520818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⋅ :@0.637021:0.537885:0.646235:0.537885:0.646235:0.522312:0.637021:0.522312:0.000000:0.000000 = :@0.667242:0.526060:0.686296:0.526060:0.686296:0.509671:0.667242:0.509671:0.000000:0.000000:0.000000 7 6 5 4! :@0.686288:0.517042:0.773893:0.517042:0.773893:0.500653:0.686288:0.500653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⋅ ⋅ ⋅ :@0.703352:0.517720:0.757050:0.517720:0.757050:0.502147:0.703352:0.502147:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4! 3!:@0.686288:0.537207:0.749366:0.537207:0.749366:0.520818:0.686288:0.520818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⋅ :@0.727345:0.537885:0.736559:0.537885:0.736559:0.522312:0.727345:0.522312:0.000000:0.000000 = 35 :@0.774132:0.526060:0.819243:0.526060:0.819243:0.509671:0.774132:0.509671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 d) :@0.502914:0.572281:0.522982:0.572281:0.522982:0.555380:0.502914:0.555380:0.000000:0.000000:0.000000 12 10 = :@0.536158:0.572281:0.601097:0.572281:0.601097:0.555892:0.536158:0.555892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C:@0.554143:0.572281:0.564057:0.572281:0.564057:0.555919:0.554143:0.555919:0.000000 12! :@0.601107:0.562919:0.703620:0.562919:0.703620:0.546530:0.601107:0.546530:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (12 – 10)! 10!:@0.601107:0.583083:0.702993:0.583083:0.702993:0.566694:0.601107:0.566694:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⋅ :@0.671980:0.583761:0.681194:0.583761:0.681194:0.568188:0.671980:0.568188:0.000000:0.000000 = :@0.711138:0.572282:0.730193:0.572282:0.730193:0.555893:0.711138:0.555893:0.000000:0.000000:0.000000 12 11 10! :@0.730186:0.563258:0.822527:0.563258:0.822527:0.546869:0.730186:0.546869:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⋅ :@0.756243:0.563936:0.765456:0.563936:0.765456:0.548363:0.756243:0.548363:0.000000:0.000000 ⋅ :@0.787477:0.563936:0.796691:0.563936:0.796691:0.548363:0.787477:0.548363:0.000000:0.000000 2! 10!:@0.730186:0.583423:0.802256:0.583423:0.802256:0.567034:0.730186:0.567034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ⋅ :@0.771243:0.584101:0.780456:0.584101:0.780456:0.568528:0.771243:0.568528:0.000000:0.000000 = 66 :@0.823374:0.572276:0.868485:0.572276:0.868485:0.555887:0.823374:0.555887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 360:@0.273229:0.744335:0.300207:0.744335:0.300207:0.727946:0.273229:0.727946:0.000000:0.000000:0.000000 30:@0.665701:0.744335:0.683686:0.744335:0.683686:0.727946:0.665701:0.727946:0.000000:0.000000 3024:@0.273229:0.822642:0.309200:0.822642:0.309200:0.806253:0.273229:0.806253:0.000000:0.000000:0.000000:0.000000 70:@0.665701:0.822642:0.683686:0.822642:0.683686:0.806253:0.665701:0.806253:0.000000:0.000000 10:@0.273229:0.902208:0.291214:0.902208:0.291214:0.885819:0.273229:0.885819:0.000000:0.000000 252:@0.665701:0.900949:0.692679:0.900949:0.692679:0.884560:0.665701:0.884560:0.000000:0.000000:0.000000