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# Easy one

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VP
Joined: 18 May 2008
Posts: 1203

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20 Jan 2009, 09:58
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Two canoe riders must be selected from each of two groups of campers. One group consists of three men and one woman, and the other group consists of two women and one man. What is the probability that two men and two women will be selected?

(A) 1/6 (B) 1/4 (C) 2/7

(D) 1/3 (E) 1/2
SVP
Joined: 07 Nov 2007
Posts: 1761
Location: New York

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20 Jan 2009, 10:10
ritula wrote:
Two canoe riders must be selected from each of two groups of campers. One group consists of three men and one woman, and the other group consists of two women and one man. What is the probability that two men and two women will be selected?

(A) 1/6 (B) 1/4 (C) 2/7

(D) 1/3 (E) 1/2

Group A : 3M 2W
Group B : 2W 1M

p = (2C2*3C2 + 2C1*1C1*3C1*2C1)/5C2*3C2
= (3+12)/10*3 = 1/2

E
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Manager
Joined: 02 Sep 2008
Posts: 103

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20 Jan 2009, 16:00
A little bit of application will surely help as a problem might not be easy for every one else.
SVP
Joined: 07 Nov 2007
Posts: 1761
Location: New York

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21 Jan 2009, 02:38
x2suresh wrote:
ritula wrote:
Two canoe riders must be selected from each of two groups of campers. One group consists of three men and one woman, and the other group consists of two women and one man. What is the probability that two men and two women will be selected?

(A) 1/6 (B) 1/4 (C) 2/7

(D) 1/3 (E) 1/2

Group A : 3M 2W
Group B : 2W 1M

p = (2C2*3C2 + 2C1*1C1*3C1*2C1)/5C2*3C2
= (3+12)/10*3 = 1/2

E

Group A : 3M 1W
Group B : 2W 1M

p = (Select 2W from GRP B and 2M from Grp A)+(Select 1W 1M from GROUP B and 1M and 1W from group A)
=(2C2*3C2 + 2C1*1C1*3C1*1C1)/4C2*3C2
= (3+6)/6*3 = 1/2
_________________

Smiling wins more friends than frowning

Re: Easy one   [#permalink] 21 Jan 2009, 02:38
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# Easy one

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