I am having trouble proving this identity:

$\displaystyle \sum_{k=0}^n$ $\displaystyle n \choose k$ $\displaystyle m - n \choose n - k$ = $\displaystyle m \choose n$

It gives a hint that you should try to interpret each of the summands.

I can't seem to use induction because there are factorials involved. And the summands don't have items that cancel out. It does seem related to a hypergeometric distribution however.

Thanks :)