Answer
The number of ways for the first evening to be made is $15,120$.
Work Step by Step
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 $15,120$.
