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:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
Top five singers, from 15 finalists. So
[tex]P_{(15,5)} = \frac{15!}{(15-5)!} = 360360[/tex]
The singers can finish first through fifth in 360360 ways.
