Answer:
You can create the schedule for the week in 19,958,400 ways.
Step-by-step explanation:
The order in which the shows are scheduled is important, which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
How many ways can you create the schedule for the week?
8 shows from a set of 12. So
[tex]P_{(12,8)} = \frac{12!}{(12-8)!} = \frac{12!}{4!} = 19958400[/tex]
You can create the schedule for the week in 19,958,400 ways.
