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.

Step-by-step 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:-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

So, the number of ways to choose 2 members out of 11 = $^{11}C_2=\dfrac{11!}{2!9!}$

$=\dfrac{11\times10}{2}=55$

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