Let $S=\sum_{k=0}^n\binom{10}{i}\binom{20}{m-i}$ where $\binom{p}{q}=0$ when $p

Question

Let $S=\sum_{k=0}^n\binom{10}{i}\binom{20}{m-i}$ where $\binom{p}{q}=0$ when $p<q$. The value of $m$, for which the value of the sum $S$ is maximum, is

Professor PC Thomas Classes · Answer

Vandermonde's identity yields maximum at $m=15$.