Question

A selection committee consisting of 10 members is to be formed from a group of 20 employees at a firm. Of the 20 employees, twelve are female. Calculate the probability that at least 8 committee members will be female.

Answer 1

Solution :

A selection committee consisting of 10 members is to be formed from a group of 20 employees at a firm. So 10 members can be selected from a group of 20 employees in 20C10 = 184756 ways.

Of the 20 employees, twelve are female so 8 are male. Suppose we want at least 8 female in the committee. This can be done in following ways,

Case 1, 8 female of 12 feamle and 2 male of 8 male can be selected in 12C8*8C2 = 13860 ways.

Case 2, 9 female of 12 feamle and 1 male of 8 male can be selected in 12C9*8C1 = 1760 ways.

Case 3, 10 female of 12 feamle and none male of 8 male can be selected in 12C10*8C0 = 66 ways.

Therefore the total number of ways to select at least 8 female in a committee are, 15686 ways.

Hence the probability that at least 8 committee members will be female is given by,

Number of ways to select at least 8 female in the committee / Total number of ways to select 10 members out of 20 employees = 15686 / 184756 = 0.0849.

The probability that at least 8 committee members will be female is 0.0849.