## Precalculus (6th Edition) Blitzer

We know that the order in which the four actors are selected makes a difference as the all the actors would be cast for a different role. Since the order matters, we use permutations. The four officers are to be selected from a club of twenty members. So, $n=20,r=4$. Hence, \begin{align} & _{20}{{P}_{4}}=\frac{20!}{\left( 20-4 \right)!} \\ & =\frac{20!}{16!} \\ & =\frac{20\times 19\times 18\times 17\times 16!}{16!} \\ & =116,280 \end{align}