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

Question

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

Quizplus · Accepted Answer

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