Question

As a television executive, you have been given 12 shows to choose from to run during your prime time slots each week. If you have 8 time slots, how many ways can you create the schedule for the week?

Answer 1

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:

$P_{(n,x)} = \frac{n!}{(n-x)!}$

How many ways can you create the schedule for the week?

8 shows from a set of 12. So

$P_{(12,8)} = \frac{12!}{(12-8)!} = \frac{12!}{4!} = 19958400$

You can create the schedule for the week in 19,958,400 ways.