Question

The club president wants to choose a social committee consisting of a chairman and two assistants. She will select them from 15 club members. How many ways can she do this?

Answer 1

Solution:

We have total 15 club members and we need to select a social committee consisting of a chairman and two assistants.

Hence, we need to select 3 member from 15 club members.

Total number of ways of selecting 3 members from a total 15 members is given by,

But we need to select a social committee from the choosen 3 members which contains a chairman and 2 assistants. Hence, arrangements of these (chairman and 2 assistants) in 3 selected members can be done by following ways :

Arrangements = (3!)/(2!) = (3×2)/(2×1) = 3

Hence, total ways of choosing a committee consisting of a chairman and two assistants = 455 × 3 = 1365

Hence, she can do this by total 1365 ways.