Question

If ${}^{22}{C}_r$ is the largest binomial coefficient in the expansion of $(1+x{)}^{22}$ then find the value of ${}^{13}{C}_r$

Answer 1

Fact: If $n$ is even, then greatest coefficient in the expansion of $(1+x{)}^n$ is ${}^n{C}_{\frac{n}{2}}$

Here $n=22$, so greatest coefficient in the expansion of $(1+x{)}^{22}$ is ${}^{22}{C}_{11}$, so $r=11$

Therefore ${}^{13}{C}_r{=}^{13}{C}_{11}=78$