a) 138
b) 128
c) 112
d) 91
Answer: d
Explanation: We first count the number of committee in which
(i). Mr. Y is a member
(ii). the ones in which he is not
case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member.
Now we are left with (6 – 1) men and (4 – 2) ladies (Mrs. X is not willing to join).
We can choose 1 more in 5+2C1 = 7 ways.
case (ii): If Mr. Y is not a member then we left with (6 + 4 – 1) people.
we can select 3 from 9 in 9C3 = 84 ways.
Thus, total number of ways is 7 + 84 = 91 ways.
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