Prove: ${n\choose 0}{m\choose k}+{n\choose 1}{m\choose {k-1}}+...+{n\choose k}{m\choose 0}={{m+n}\choose k}$
How to prove Vandermonde's Identity: $\sum_{k=0}^{n}\binom{R}{k}\binom{M}{n-k}=\binom{R+M}{n}$?