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# Two representatives must be selected from each of two groups of studen

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Joined: 31 Oct 2010
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Two representatives must be selected from each of two groups of studen  [#permalink]

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07 Dec 2010, 05:42
1
00:00

Difficulty:

75% (hard)

Question Stats:

48% (02:20) correct 52% (02:54) wrong based on 45 sessions

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Two representatives must be selected from each of two groups of students. 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 2 men and 2 women will be selected ?

A. 1/6
B. 1/4
C. 2/7
D. 1/3
E. 1/2
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Posts: 64174
Re: Two representatives must be selected from each of two groups of studen  [#permalink]

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07 Dec 2010, 06:09
tomchris wrote:
two representatives must be selected from each of two groups of students . 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 2 men amd 2 women will be selected ?

a) 1/6
b) 1/4
c) 2/7
d) 1/3
e) 1/2

Group #1: {m1, m2, m3, w1};
Group #2: {m4, w2, w3}.

There are following cases possible to select 2m and 2w:
Both men from group #1 and both women from group #2: $$C^2_3*C^2_2=3$$;
One man and one women from each group: $$(C^1_3*C^1_1)*(C^1_1*C^1_2)=6$$;

Total ways to select 2 persons from group #1 and group #2 is $$C^2_4*C^2_3=18$$;

$$P=\frac{# \ of \ favorable \ outcomes}{total \ # \ of \ outcomes}=\frac{3+6}{18}=\frac{1}{2}$$.

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Re: Two representatives must be selected from each of two groups of studen  [#permalink]

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05 Feb 2016, 10:28
tomchris wrote:
Two representatives must be selected from each of two groups of students. 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 2 men and 2 women will be selected ?

A. 1/6
B. 1/4
C. 2/7
D. 1/3
E. 1/2

Group 1: 3 Men and 1 Woman
Group 2: 1 Men and 2 Woman

Need: 2 Men and 2 women

Case 1: 2 Men from Group 1 and 2 women from group 2 - 3C2*2C2 = 3 ways
Case 2: 1 Men and 1 Woman from Group 1 and 1 Man and 1 women from group 2 - 3*1*1*2 = 6 ways

Total Favorable cases = 3+6 = 9

Total Possible ways of selecting students 2 from each group = 4C2*3C2 = 6*3 = 18

Probability = 9/18 = 1/2

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Re: Two representatives must be selected from each of two groups of studen   [#permalink] 05 Feb 2016, 10:28