## Precalculus (6th Edition) Blitzer

The number of ways for the first evening to be made is $15,120$.
We know that from the information, \begin{align} & n=9 \\ & r=5 \\ \end{align} Then, we have to find the number of permutations of 9 things taken 5 at a time: \begin{align} & {}_{9}{{P}_{5}}=\frac{9!}{\left( 9-5 \right)!} \\ & =\frac{9!}{4!} \\ & =\frac{9\times 8\times 7\times 6\times 5\times 4!}{4!} \\ & =15,120 \end{align} Thus, the number of ways is $15,120$.