Question

How many different three-member teams can be formed from six students?

Answer 1

There are `20` ways to choose 3 students from a group of 6 students.

Explanation:

For this question, you need to choose `3` students from a group of `6` students. Since no two students are the same, you will need to determine the number of combinations.

To do so, simply do `(n!)/(r!(n-r)!)` where `n` is the number of students total and `r` is the number of students that need to be chosen.

Plugging in, we get:

`(6!)/(3!(6-3)!)`
`=(6*5*4*3*2*1)/((3*2*1)(3!))`
`=(6*5*4*cancel(3*2*1))/(cancel((3*2*1))(3*2*1))`
`=5*4`
`=20`

So, there are `20` ways to choose 3 students from a group of 6 students.