Question

A committee consisting of 3 faculty members and 5 students is to be formed. Every committee position has the same duties and voting rights. There are 7 faculty members and 11 students eligible to serve on the committee. In how many ways can the committee be formed?

Answer 1

In 16170 ways the committee can be formed.

Explanation:

3 faculty members and 5 students are required to form a committee.

The eligible to serve on the committee are 7 faculty members and 11 students.

If each committee position has the same duties and voting rights.

Then, the number of ways of selecting 3 faculty members out of 7 eligible faculty members is
`^7C_(3) = 35`.

Again, the number of ways of selecting 5 students out of 11 eligible students is given by
`^(11)C_(5) = 462`.

Therefore, in (35 × 462) = 16170 ways the committee can be formed. (Answer)