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A golf club has 12 boys and 16 girls, from whom, a committee

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Director
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Joined: 13 Nov 2003
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A golf club has 12 boys and 16 girls, from whom, a committee [#permalink] New post 23 Mar 2004, 07:00
A golf club has 12 boys and 16 girls, from whom, a
committee of 2 boys and 2 girls has to be formed. The probability that
the club members Peter (boy) and Mary (girl) will always be included
in the committee is:

(1)13/240
(2)17/185
(3)19/82
(4)15/121
(5)11/315
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Joined: 15 Dec 2003
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 [#permalink] New post 23 Mar 2004, 10:11
I've been pondering on this question for a while. I wonder if there's not any error in the answer choices.
# of ways to form a team when P+M are in the team: 11C1 * 15C1 = 165
# of ways to form a team of 2 boys+2 girls: 12C2*16C2 = 7920
Prob. of forming a team with both P+M: 165/7920 = 1/48
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 [#permalink] New post 23 Mar 2004, 11:15
Hallo guys, the official answer is 11C1x15C1/28C4 or 5). I also got 1/48, may be the answer is incorrect.
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 [#permalink] New post 23 Mar 2004, 11:18
It can't be 28C4 because this would mean that the team could be form of 4 people of ANY gender. We need to isolate boys and girls apart with 12C2*16C2 as denominator
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Paul

  [#permalink] 23 Mar 2004, 11:18
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A golf club has 12 boys and 16 girls, from whom, a committee

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