# Math Help - Combinatorial proof

1. ## Combinatorial proof

By a combinatorial argument, prove that for $r \leq n$ and $r \leq m$, $\binom {n+m} {r} = \binom {m} {0} \binom {n} {r} + \binom {m} {1} \binom {n} {r-1} + ... + \binom {m} {r} \binom {n} {0}$.

2. Hint - To select r objects from (n+m) objects - break (n+m) objects in two groups (n) and (m) objects. How will you go about selecting r objects in total now (from both the groups)?