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?

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? Correct Answer 91

We first count the number of committee in which(i). Mr. Y is a member (ii). the ones in which he is notCase (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 in5+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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