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In how many ways can a group of 3 people be selected

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In how many ways can a group of 3 people be selected [#permalink]

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09 Nov 2012, 10:59
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Question Stats:

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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
[Reveal] Spoiler: OA
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Re: In how many ways can a group of 3 people be selected [#permalink]

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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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Re: In how many ways can a group of 3 people be selected [#permalink]

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10 Nov 2012, 04:48
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derekgmat wrote:
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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Re: In how many ways can a group of 3 people be selected [#permalink]

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12 Nov 2012, 01:45
Bunuel wrote:
derekgmat wrote:
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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Re: In how many ways can a group of 3 people be selected [#permalink]

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28 Dec 2012, 05:05
derekgmat wrote:
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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Re: In how many ways can a group of 3 people be selected [#permalink]

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01 Sep 2016, 03:32
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Re: In how many ways can a group of 3 people be selected   [#permalink] 01 Sep 2016, 03:32
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