Question

A swim team must be chosen from 10 candidates. What is the greatest number of different four-person teams that can be chosen?

Answer 1

There are a total of 210 different four-person teams that could be chosen.

Explanation:

In order to calculate the greatest number of different four-person teams we need to calculate the combination of 10 people taken four by four as shown below:

`C_(10,4) = (10!)/(4!(10 - 4)!)\\C_(10,4) = (10!)/(4!*6!)\\C_(10,4) = (10*9*8*7*6!)/(4!*6!)\\C_(10,4) = (10*9*8*7)/(4*3*2)\\C_(10,4) = (5040)/(24) = 210`

There are a total of 210 different four-person teams that could be chosen.