Question

Evaluate $\frac{n!}{(n-r)!}$, when
(i) $n=6,r=2$.

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

Answer 1

We need to find value of $\frac{n!}{(n-r)!}$

i) Given, $n=6,r=2$

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

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

$=\frac{6\times 5\times 4!}{4!}=30$

ii) Given, $n=9,r=5$

Therefore the value of $\frac{n!}{(n-r)!}=\frac{9!}{(9-5)!}=\frac{9!}{4!}=\frac{9\times 8\times 7\times 6\times 5\times 4!}{4!}$
$=9\times 8\times 7\times 6\times 5=15120$