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

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A golf club has 12 boys and 16 girls, from whom, a committee [#permalink]

23 Mar 2004, 08:00

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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23 Mar 2004, 11:11

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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Paul

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23 Mar 2004, 12:15

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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23 Mar 2004, 12:18

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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[#permalink] 23 Mar 2004, 12:18

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

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

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

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