## Thinking Mathematically (6th Edition)

$720$ different ways
A schedule is an arrangement, an ordered list ... Order matters, we use permutations. Permutations Formula: The number of permutations possible if $r$ items are taken from $n$ items is ${}_{n}P_{r}=\displaystyle \frac{n!}{(n-r)!}$ The number of acts chosen are r=6 from a total of n=6 acts ${}_{6}P_{6}=\displaystyle \frac{6!}{(6-6)!}=\frac{6!}{0!}\qquad$... by definition $0!=1$ $=6\times 5\times 4\times 3\times 2\times 1$ $=720$