Question

Compute: $\left(i\right)\frac{7!}{5!}\left(ii\right)\frac{12!}{(10!)(2!)}$

Answer 1

$\because n!=n(n-1)(n-2)\cdots 3\cdot 2\cdot 1$

$\left(i\right)\frac{7!}{5!}=\frac{7\times 6\times 5!}{5!}=42$

$\left(ii\right)\frac{12!}{(10!)(2!)}=\frac{12\times 11\times 10!}{(10!)\times 2!}=\frac{12\times 11}{2\times 1}=66$