Question

Evaluate $\frac{n!}{(n-r)!}$ when

$\left(i\right)n=6,r=2\left(ii\right)n=9,r=5.$

Answer 1

(i) Here $n=6$ and $r=2$

$\therefore \frac{n!}{(n-r)!}=\frac{6!}{(6-2)!}=\frac{6!}{4!}$

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

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

$\therefore \frac{n!}{(n-r)!}=\frac{9!}{(9-5)!}=\frac{9!}{4!}$

$=\frac{9\times 8\times 7\times 6\times 5\times 4!}{4!}=15120.$