(10 points) From a group of 9 men and 7 women a committee consisting of 4 men and 4 women is to be formed. How many different committees are possible if (a) 2 of the men refuse to serve together? (a) 2 of the women refuse to serve together? (a) 1 man and 1 woman refuse to serve together?

a) 2450

b) 1890

c) 1050

Step-by-step explanation:

Given:

- Available Group = 9 M & 7 F

- Committee of= 4 M and 4 W to be formed

Find:

- (a) 2 of the men refuse to serve together?

- (a) 2 of the women refuse to serve together?

- (a) 1 man and 1 woman refuse to serve together?

Solution:

- The question pertains to a selection process, We will use combinations for each case as follows.

part a)

- Since 2 men cant be selected together. Then we have to discount for one man while selecting Man for the committee. Hence, the combinations are:

                                   8C4 x 7C4 = 2450

part b)

- Since 2 women cant be selected together. Then we have to discount for one woman while selecting them for the committee. Hence, the combinations are:

                                   9C4 x 6C4 = 1890

part b)

- Since 1 women and a man cant be selected together. Then we have to discount for one woman and one man while selecting them for the committee. Hence, the combinations are:

                                   8C4 x 6C4 = 1050