Question

- Determina el valor de estos números combinatorios​

Answer 1

Respuesta:

Explicación paso a paso:

a )  $( {{6} \atop {3}} )$

$( {{m} \atop {n}} ) = \frac{m!}{n!(m-n)!}$

$({ {{6} \atop {3}} ) = \frac{6!}{3!(6-3)!} =\frac{6*5*4*3!}{3*2*1*3!} = \frac{120}{6} =20$

b )   $({{7} \atop {7}} )$

$( {{7} \atop {7}} ) = \frac{7!}{7!(7-7)!} =\frac{7!}{7! *0!} = \frac{1}{1} = 1$                            (  0! = 1  )

c )   $({ {{9} \atop {4}} )$

 $({ {{9} \atop {4}} ) =\frac{9!}{4!(9-4)!} = \frac{9*8*7*6*5!}{4*3*2*1*5!} =\frac{3024}{24} = 126$

d )  $({ {{7} \atop {2}} )$

$({ {{7} \atop {2}} )=\frac{7!}{2!(7-2)!} = \frac{7*6*5!}{2*1*5!} =\frac{42}{2} =21$

e )  $({ {{8} \atop {4}} )$

$( {{8} \atop {4}} ) = \frac{8!}{4! (8-4)!} = \frac{8*7*6*5*4!}{4*3*2*1*4!} =\frac{1680}{24} =70$

f ) $({ {{10000} \atop {9999}} )$

$({{10000} \atop {9999}} ) =\frac{10000!}{9999! (10000-9999)!} =\frac{10000*9999!}{9999!*1!} = \frac{10 000 }{1} = 10000$