How many ways can a committee of four students be selected from a 15-member club?

Solution:

To form a committee it is enough if we select four students from the existing 15.

Hence it is a problem under combination

Now selection of 4 from 15 is = ¹⁵C₄

= (15!)/(15 - 4)! × (4!)

= (15 × 14 × 13 × 12 × 11!)/(11!)(4 × 3 × 2 × 1)

= 1365

Example:

Let us find the ways to form a committee under the following cases

(i) If the committee has 8 students

Then it is selection of 8 students from 15 is ¹⁵C₈

= (15!)/(15 - 8)! × (8!)

= (15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7!)/(7!)((8!)

= 6435

---

How many ways can a committee of four students be selected from a 15-member club?

Summary:

Committee of four students be selected from a 15-member club = 1365