Question

A committee has seven men and four women. If four people are selected to go to a conference, what is the chance that the group is two men and two women?

Answer 1

Given:

A committee has seven men and four women.

four people are selected to go to a conference

We will use the combinations as follows

the number of ways to choose the four people are:

`7C4+7C3+7C2+7C1+7C0`

The rule of combinations is:

`\text{nCr}=(n!)/((n-r)!\cdot r!)`

so, the number of ways will be:

`35+35+21+7+1=99`

The number of ways to make a group of two men and two women will be:

`7C2=21`

So, the chance that the group is two men and two women =

`(21)/(99)=(7)/(33)`

so, the answer will be 7/33