Prove the following identity (using a combinatorial proof if possible). The identity is called Vandermonde’s identity.

\[\binom{n+m}{r} = \binom{n}{0}\binom{m}{r} + \binom{n}{1}\binom{m}{r-1} + \binom{n}{2}\binom{m}{r-2} + ... + \binom{n}{r}\binom{m}{0}\]

TBD