Question

How many different committees can be formed from 6 teachers and 37 students if the committee consists of 4 teachers and 4 ​students?

The committee of 8 members can be selected in
BLANK different ways.

Answer 1

The committee of 8 members can be selected in 990,675 different ways.

Explanation:

The order in which the teachers and the students are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

In this question:

4 teachers from a set of 6.

4 students from a set of 37.

Then

`T = C_(6,4)C_(37,4) = (6!)/(4!2!) * (37!)/(4!33!) = 990675`

The committee of 8 members can be selected in 990,675 different ways.