Answer
$8,648,640$ arrangements
Work Step by Step
A permutation from a group of items occurs when no item is used more than once and the order of arrangement makes a difference.
The number of permutations possible if $r$ items are taken from $n$ items is
${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$.
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Order of selecting songs (arrangements) is important, so we deal with permutations
of r=7 songs to be taken from n=13.
The formula ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$ applies.
${}_{13}P_{7}=\displaystyle \frac{13!}{6!}=13\times 12\times 11\times 10\times 9\times 8\times 7$
$=8,648,640$ arrangements