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?
Options:
A . 138
B . 128
C . 112
D . 91
Answer: Option D 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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