SOLUTION: A committee is to be formed comprising of 7 member such that there is a majority of men and at least 1 woman in every committee.The shortlist consists of 9 men and 6 women.In how m

Question 1135741: A committee is to be formed comprising of 7 member such that there is a majority of men and at least 1 woman in every committee.The shortlist consists of 9 men and 6 women.In how many ways can this be done?

Answer by VFBundy(438) (Show Source): You can put this solution on YOUR website!
The problem states that the committee must have a majority of men AND have at least one woman. That means the committee must be comprised of six men and one woman, five men and two women, or four men and three women.

Ways a committee with 6 men and 1 woman could be formed:
9C6 * 6C1 = 84 * 6 = 504

Ways a committee with 5 men and 2 women could be formed:
9C5 * 6C2 = 126 * 15 = 1890

Ways a committee with 4 men and 3 women could be formed:
9C4 * 6C3 = 126 * 20 = 2520

Add all these together: 504 + 1890 + 2520 = 4914.

So, there are 4914 different possible combinations.
RELATED QUESTIONS
Out of 8 women and 7 men a committee of 3 women and 4 men is to be formed. Mrs. X should... (answered by lynnlo)

Out of 6 women and 8 men , a committee consisting of 4 woman and 5 men is to be... (answered by greenestamps)

A committee of 3 is to be selected from a group comprising 8 women and 5 men. In how many (answered by TimothyLamb,ewatrrr)

The board of directors of Saner Automatic Door Company consists of 12 members, 3 of whom... (answered by edjones)

A committee of 5 people is selected from a group of 7 men and 8 women. In how many ways... (answered by ikleyn)

There are 12 women and 5 men. A committee of 7 women and 4 men is to be chosen. How many... (answered by SUNIL1987MAURYA)

A commitee of 6 members is formed out of 7 men and 5 women.how many commitees can be... (answered by ewatrrr)

Suppose that there are 7 women and 5 men in a department. a). How many ways a... (answered by greenestamps)

A 6-member committee is to be formed in a hospital unit that has 8 RNs and 4 LPNs. If the (answered by math_tutor2020)