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# A committe of three students has to be formed. There are

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Senior Manager
Joined: 05 Jun 2005
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A committe of three students has to be formed. There are [#permalink]  29 Oct 2006, 22:29
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A committe of three students has to be formed. There are five students: Jane, Joan, Paul, Stuart and Jessica. If Paul and Stuart refuse to in the committee together and Jane refuses to be in the committe without Paul, how many committee are possible?

1) 3
2) 4
3) 5
4) 6
5) 8
Manager
Joined: 25 Sep 2006
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B

Paul and Stuart mutually exclusive, (<-- did I interpret this right?)

Commitee with Paul
Paul +
{ Jane, Joan, Jess }
The commitee will be without one of them
3 possible combo

Commitee with Stuart
Stuart +
{ Joan, Jess}
Thats it, this is the only possible combo with Stuart

Commitee without both Stuart and Paul
{ Joan, Jess}
No combination of three availble

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Quote:
A committe of three students has to be formed. There are five students: Jane, Joan, Paul, Stuart and Jessica. If Paul and Stuart refuse to in the committee together and Jane refuses to be in the committe without Paul, how many committee are possible?

1) 3
2) 4
3) 5
4) 6
5) 8

Ans: B

First Selection:
If Jane is in the committee, then Paul is also present so we have

Ja:P:_

for the last place we have 2 options (Je and Jo) and one place i.e. 2C1 so for this selection 1*2 = 2 options

Second Selection:

If P is there then we can have Jo, and Jes for the other two locations i.e
P:_: _ so two choice for two locations i.e. 1*2c2 = 1

I have not counted Jane here because then it will be the same as the first selection.

Third Selection:

If stuart is there again then we can Je and Jo, we cant have Paul and Jane. so for this again 1 selection.

So the total are 4 selections.
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