Question

Calcule:
A) C10,3
B) A9,3

Answer 1

a) $C_{n,p} = \frac{n!}{p!(n-p)!}$
$C_{10,3} = \frac{10!}{3!(10-3)!}$
$C_{10,3} = \frac{10!}{3!7!}$
$C_{10,3} = \frac{10*9*8*7!}{3!7!}$               Elimina o '7!'
$C_{10,3} = \frac{10*9*8}{3!}$
$C_{10,3} = \frac{720}{6}$
$C_{10,3} =$ 120

b) $A_{n,p} = \frac{n!}{(n-p)!}$
$A_{9,3} = \frac{9!}{(9-3)!}$
$A_{9,3} = \frac{9!}{6!}$
$A_{9,3} = \frac{9*8*7*6!}{6!}$               Elimina o '6!'
$C_{10,3} =$ 9 * 8 * 7
$C_{10,3} =$ 504

Espero ter lhe ajudado =)