Question

First- , second- , and third-place prizes are to be awarded in a couples dance contest in which 34 contestants are entered. In how many ways can the prizes be awarded?

Answer 1

The prizes can be awarded in 35904 ways.

Explanation:

The order is important.

For example, John winning prize A, Laura prize B and Jonathan prize C is a different outcome than Laura winning prize A, John winning prize B and Jonathan winning prize C.

So we use the permutations formula to solve this problem:

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 how many ways can the prizes be awarded?

Three prizes divided among 34 contestants. So

`P_((34,3)) = (34!)/((34-3)!) = (34!)/(31!) = 35904`

The prizes can be awarded in 35904 ways.