Question

There were 15 students running in a race. How many different arrangements of first, second, and third place are possible?

Answer 1

The area 2730 possible arrangements of first, second, and third place.

Explanation:

The order in which the students finish is important. For example A, B and C is a different finishing order(outcome) than B, A and C. 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)) = (n!)/((n-x)!)`

In this question:

3 from a set of 15. So

`P_((15,3)) = (15!)/((15-3)!) = 2730`

The area 2730 possible arrangements of first, second, and third place.