Essay

$\text { Prove for all integers } n , k \text {, and } r \text { with } n \geq k \geq r \text { that } \left( \begin{array} { l } n \\k\end{array} \right) \left( \begin{array} { l } k \\r\end{array} \right) = \left( \begin{array} { l } n \\r\end{array} \right) \left( \begin{array} { l } n - r \\k - r\end{array} \right) \text {. }$