Vandermonde type identity for JEE

Formula

\(\displaystyle \sum_{k=0}^{r} {}^mC_k\,{}^nC_{r-k}={} ^{m+n}C_r\)

Variables: \(m,n,r\) are non-negative integers.

Conditions: Terms with invalid lower indices are treated as zero.

Advanced combinatorial sums and coefficient comparison.