Question

Find the value of ${}^{10}{C}_5+2.{(}^{10}{C}_4){+}^{10}{C}_3$.

Answer 1

${}^{10}{C}_5+2.{(}^{10}{C}_4){+}^{10}{C}_3=\frac{10!}{5!.5!}+2.\frac{10!}{6!.4!}+\frac{10!}{7!.3!}=252+420+120=792$