From a total of six men and four ladies a committee of three is to be formed. If Mrs. X is not willing to join the committee in which Mr. Y is a member, whereas Mr.Y is willing to join the committee only if Mrs Z is included, how many such committee are possible?

A. 138

B. 128

C. 112

D. 91

Answer: Option D

Solution(By Examveda Team)

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.