Vandermonde-type identity for JEE

Formula

\[\sum_{r=0}^{k}{m\choose r}{n\choose k-r}={m+n\choose k}\]

Variables: \(m,n\) are non-negative integers; \(k\) is an integer.

Conditions: Terms with invalid lower indices are taken as zero; effectively \(0\le k\le m+n\).

Coefficient extraction in products of binomials.