A committee is to be formed comprising 7 members such that there is a simple majority of men and at least 1 woman. The shortlist consists of 9 men and 6 women. In how many ways can this committee be formed?
A.4914
B.3630
C.3724
D.3824
Answers
Answer:
Ans = 4914
Step-by-step explanation:
Number of members of the committee = 7
Condition is, Men should have the majority and at least 1 woman should be present.
∴ Number of man >= 4 [to maintain a majority]
and, Number of women <=3 and >=1 [to maintain majority as well as a single women should be present]
Given, Total men = 9 & Total Women = 6
Now, we have to select men out of 9 men and women from 6 nos. or women.
So, possible cases of forming the committee are as follows:
Case 1: 6 men and 1 woman
Number of ways committee can be formed = Selecting 6 men out of 9 men + Selecting 1 woman out of 6 woman
= 9C6 x 6C1 = 504
Case 2: 5 men and 2 woman
Number of ways committee can be formed = 9C5 x 6C2 = 1890
Case 3: 4 men and 3 woman
Number of ways committee can be formed = 9C4 x 6C3 = 2520
If we go further, the condition of majority of men will be violated.
∴ Total no. of ways the committee can be formed is
= Case 1 + Case 2 + Case 3
= 504 + 1890 + 2520
= 4914 = Ans