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

Answer:

The prizes can be awarded in 35904 ways.

Step-by-step 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:

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

In how many ways can the prizes be awarded?

Three prizes divided among 34 contestants. So

$P_{(34,3)} = \frac{34!}{(34-3)!} = \frac{34!}{31!} = 35904$

The prizes can be awarded in 35904 ways.