Question

Problem 4. Solve the following counting problems. (a) How many committees of size 6 can be formed by a club consisting of 15 people?

Answer 1

5005

Explanation:

In the question we have to form a committee of six from a club of consisting of 15 people.

This a simple case of selection of six people from a group of 15 people.

which can be done in

`^(15)C_6= (15!)/(6!*9!)=5005`

hence, the number of ways of forming committees of size six from a club of 15 members= 5005