Question

A committee is to consist of two members. If there are five men and six women

available to serve on the committee, how many different committees can be
formed?

Answer 1

Answer: The number of different committees can be formed = 55.

Explanation:

Given: Number of members in a committee = 2

There are five men and six women available to serve on the committee.

That means, Total persons available to serve on the committee = 5+6=11

Number of combinations of choosing r things from n things is given by:-

`^nC_r=(n!)/(r!(n-r)!)`

So, the number of ways to choose 2 members out of 11 =
`^(11)C_2=(11!)/(2!9!)`

`=(11*10)/(2)=55`

Hence, the number of different committees can be formed = 55