Question

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

Answer 1

$\left(i\right)$ when $n=6$ and $r=2$

$\frac{n!}{(n-r)!}=\frac{6!}{(6-2)!}$
$=\frac{6\times 5\times 4!}{4!}$
$=6\times 5=30$

$\left(ii\right)$ when $n=9$ and $r=5$
$\frac{n!}{(n-r)!}=\frac{9!}{(9-5)!}$
$=\frac{9\times 8\times 7\times 6\times 5\times 4!}{4!}$
$=9\times 8\times 7\times 6\times 5$
$=15120$