Question

Ten field hockey teams are competing in a tournament. Only the top three teams will be recognized as the first place, second place and third place winners. In how many ways could the ranking of the top three teams occur?

Answer 1

Answer:

The ranking of the top three teams could occur in 720 ways.

Step-by-step explanation:

The order in which the teams are ranked is important, that is, for example, Oilers, Flames and Canucks is a different outcome of Oilers, Canucks and Flames. This means that the permutations formula is used 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 how many ways could the ranking of the top three teams occur?

Three teams from a set of 10. So

$T = P_{(10,3)} = \frac{10!}{7!} = 720$

The ranking of the top three teams could occur in 720 ways.