blaster wrote:A committee of three students has to be formed. There are five candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?
According to me the answer is
4 teams
Plz advise whether it is correct.
The approach is as below.
Lets start with Jane
1) If Jane is there in the committee, even Paul has to be there.
Jane+Paul+third member
Third member cannot be Stuart.So the third member can be either Joan or Jessica
So the two two teams can be as below
Jane+Paul+Jessica
Jane+Paul+Joan
2) If we start forming a community with Joan, then
a) if we add Jane we will have to add hence same as 1)
b) if we add Paul then we have then we have two options for the third member--Jane/Jessica.we can't take stuart
We have already considered Jane in 1) Hence the new team can be
Joan+Paul+Jessica
c) if we add stuart then we have then we have only one option for the third member i.e Jessica.we can't take stuart. He the new team can be
Joan+Staurt+Jessica
Repeating the same procedure for remaining three members we come to the conclusion that no more new teams apart from the above 4 can be formed.
Hence the answer is 4.
