Question

Evaluate $\frac{n!}{\left(n-r\right)!}$, when
(i) n = 6, r = 2**(ii)** n = 9, r = 5

Answer 1

(i) When n = 6, r = 2,

$\frac{n!}{(n-r)!}=\frac{6!}{(6-2)!}$

$=\frac{6!}{4!}=\frac{6\times5\times4!}{4!}$

$=30$

(ii) When n = 9, r = 5,

$\frac{n!}{(n-r)!}=\frac{9!}{(9-5)!}$

$=\frac{9!}{4!}=\frac{9\times8\times7\times6\times5\times4!}{4!}$

$=9\times8\times7\times6\times5=15120$