Question

simplifique as expressões.
a) C3,1.C8,2

b) Cn+1,n


c) Cn,p.(n-p)!

Answer 1

O símbolo C(n,m), sendo n e m números naturais, representa a combinação simples, dada pela expressão:

C(n,m) = n!/(n-m)!m!

Assim, podemos aplicar as expressões:

a) C(3,1) * C(8,2) = [3!/(3-1)!1!] * [8!/(8-2)!2!]

C(3,1) * C(8,2) = [3!/2!1!] * [8!/6!2!]

C(3,1) * C(8,2) = [3*2!/2!*1] * [8*7*6!/6!2*1]

C(3,1) * C(8,2) = 3 * 8*7/2

C(3,1) * C(8,2) = 84

b) C(n+1,n) = (n+1)!/(n+1-n)!n!

C(n+1,n) = (n+1)*n!/1!n!

C(n+1,n) = n+1

c) C(n,p) * (n-p)! = [n!/(n-p)!p!] * (n-p)!

C(n,p) * (n-p)! = n!/p!