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

Answer:

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

Step-by-step 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.

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

In this question:

4 teachers from a set of 6.

4 students from a set of 37.

Then

$T = C_{6,4}C_{37,4} = \frac{6!}{4!2!} \times \frac{37!}{4!33!} = 990675$

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