There is a committee to be selected comprising of 5 people from a group of 5 men and 6 women. Whether the selection is randomly done then determines the possibility of having the given possibilities combinations

i. One particular man and one particular woman should not be in the committee (one man four women)

Solution

i. P(one particular man and one particular woman should not be in the committee would be determined as given below:

The group size = 5m + 6w

Committee size = 5 people

Actual groups size from which to

Select the committee =  4m + 5w

Committee = 1m + 4w

The committee may be selected in ⁹C₅

The one man may be selected in ⁴C₁ ways

The four women may be selected in ⁵C₄ ways

∴ P(committee of 4w1man).

 (⁵C₄ * ⁴C₁) = ⁹C₅

= 10/63