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derekgmat
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In how many ways can a group of 3 people be selected 09 Nov 2012, 10:59
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Difficulty:

25% (medium)

Question Stats:

79% (01:51) correct 21% (01:55) wrong based on 180 sessions

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In how many ways can a group of 3 people be selected out of 5 men and 7 women, so that 2 of them are of the same gender?

(A) 96
(B) 125
(C) 155
(D) 175
(E) 225
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D
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Javoni
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In how many ways can a group of 3 people be selected 09 Nov 2012, 13:12
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Since the question stem asks for 2 members of the same gender we get the following:
1. 2-Men and 1-Woman, hence (2C5)*(1C7) = 5*2*7=70
2. 2-Women and 1-Man, hence (2C7)*(1C5) = 7*3*5 =105
Thus, the total number of ways would be: 70+105=175

Please, correct me, if I went awry
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In how many ways can a group of 3 people be selected 10 Nov 2012, 04:48
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derekgmat
In how many ways can a group of 3 people be selected out of 5 men and 7 women, so that 2 of them are of the same gender?

(A) 96
(B) 125
(C) 155
(D) 175
(E) 225

Alternatively one can do:
The total number of committees of 3 possible out of 12 people without restrictions: \(C^3_{12}=220\);
The number of committees with all men: \(C^3_5=10\);
The number of committees with all women: \(C^3_7=35\);

Thus the answer is 220-(10+35)=175.

Answer: D.
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In how many ways can a group of 3 people be selected 12 Nov 2012, 01:45
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Bunuel
derekgmat
In how many ways can a group of 3 people be selected out of 5 men and 7 women, so that 2 of them are of the same gender?

(A) 96
(B) 125
(C) 155
(D) 175
(E) 225

Alternatively one can do:
The total number of committees of 3 possible out of 12 people without restrictions: \(C^3_{12}=220\);
The number of committees with all men: \(C^3_5=10\);
The number of committees with all women: \(C^3_7=35\);

Thus the answer is 220-(10+35)=175.

Answer: D.

To make this question clearer, i think it should be stated more precisely "exactly 2 of them are of the same gender" otherwise one could understand that commetees consisting of just men and/or just women are possible. Don't you think so Bunuel?
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In how many ways can a group of 3 people be selected 28 Dec 2012, 05:05
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derekgmat
In how many ways can a group of 3 people be selected out of 5 men and 7 women, so that 2 of them are of the same gender?

(A) 96
(B) 125
(C) 155
(D) 175
(E) 225

M M W = \(=\frac{5!}{2!3!} * \frac{7!}{6!1!} = 10 * 7 = 70\)
W W M = \(=\frac{7!}{2!5!} * \frac{5!}{1!4!} = 21 * 5 = 105\)

\(70 + 105 = 175\)

Answer: D
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In how many ways can a group of 3 people be selected 22 May 2025, 07:06
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