Sum over k of r Choose k by s Choose k by k

Theorem
Let $s \in \R, r \in \Z_{\ge 0}$.

Then:
 * $\displaystyle \sum_k \binom r k \binom s k k = \binom {r + s - 1} {r - 1} s$

where $\dbinom r k$ etc. are binomial coefficients.