Combinatorics and Graph Theory · Problem 1.3.14

Fundamentals — David Guichard

Mathematics — Combinatorics · vandermonde-identity

Problem

Give a combinatorial proof of

\displaystyle\sum_{i=0}^{k} \binom{m}{i}\binom{n}{k-i} = \binom{m+n}{k}

. Rewrite this identity in simpler form if

m = n

, and when

k = m = n