Question

there are 15 finalist in a singing competition. the top five singers receive prizes. how many ways can the singer finish first through fifth

Answer 1

Answer:

The singers can finish first through fifth in 360360 ways.

Step-by-step explanation:

The order of the singers is important, because they are ranked by positions. So we use the permutations formula 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:

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

In this question:

Top five singers, from 15 finalists. So

$P_{(15,5)} = \frac{15!}{(15-5)!} = 360360$

The singers can finish first through fifth in 360360 ways.