Prove the identity $\binom{n}{r}\binom{r}{k} = \binom{n}{k}\binom{n−k}{r−k} ,$ whenever $n, r,$ and $k$ are nonnegative integers with $r \leq n$ and $k \leq r,$
- using a combinatorial argument.
- using an argument based on the formula for the number of $r$-combinations of a set with $n$ elements.
