Question

A club consisting of 6 juniors and 8 seniors is to be formed from a group of 13 juniors and 16 seniors. How many different clubs can be formed from the group?

Answer 1

22,084,920 different clubs can be formed from the group

Explanation:

The order in which the students are chosen to the club is not important. So we use the combinations formula 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:

6 juniors, from a set of 13.

8 seniors, from a set of 16.

So

`T = C_(13,6)*C_(16,8) = (13!)/(6!(13-6)!)*(16!)/(8!(16-8)!) = 22084920`

22,084,920 different clubs can be formed from the group