Product of r Choose m with m Choose k

Theorem
Let $$r \in \R, m \in \Z, k \in \Z$$.

Then:
 * $$\binom r m \binom m k = \binom r k \binom {r - k} {m - k}$$

where $$\binom r m$$ is a binomial coefficient.

Proof
Let $$r \in \Z$$.

Then:

$$ $$ $$ $$