Answer
The number of ways to schedule five performances out of nine = $9_{{P}{_{5}}}$ = 15,120
Work Step by Step
Total number of performances = 9
Number of performances performed on first evening = 5
To find the number ways to schedule performance on first evening when the order performance is important, we use the formula $n_{{P}{_{r}}}$ = $\frac{n!}{(n - r)! }$
The number of ways to schedule five performances out of nine = $9_{{P}{_{5}}}$ = $\frac{9!}{(9 - 5)!}$
= $\frac{9!}{4!}$
= $\frac{9\times8\times7\times6\times5\times4!}{4!}$
= $9\times8\times7\times6\times5$
= 15,120
