Chapter 5, Problem 29E

To determine

To prove: The formula ${\displaystyle \sum _{\begin{array}{l}r,s,t\ge 0\\ r+s+t=n\end{array}}^{}\left(\begin{array}{c}{m}_1\\ r\end{array}\right)\left(\begin{array}{c}{m}_2\\ s\end{array}\right)\left(\begin{array}{c}{m}_3\\ t\end{array}\right)}$, Where the summation spreads over all nonnegative integers $r,s\text{ and }t$ with sum $r+s+t=n$.