Answer
The number of different ways to line up the bands to perform at a benefit concert is 15120.
Work Step by Step
We need to choose 5 bands from a group of 9 bands. The order in which the bands are chosen matters because one band can perform only once. Therefore, we need to find the number of permutations of 9 things taken 5 at a time.
We apply the formula,
${}_{n}{{P}_{r}}=\frac{n!}{\left( n-r \right)!}$
Where $ n=9,r=5$
$\begin{align}
& {}_{9}{{P}_{5}}=\frac{9!}{\left( 9-5 \right)!} \\
& =\frac{9!}{4!}
\end{align}$
Solve further to get,
$\begin{align}
& {}_{9}{{P}_{5}}=\frac{9\times 8\times 7\times 6\times 5\times 4!}{4!} \\
& =9\times 8\times 7\times 6\times 5 \\
& =15120
\end{align}$
