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

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Intern
Joined: 07 Nov 2012
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In how many ways can a group of 3 people be selected [#permalink]  09 Nov 2012, 09:59
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:14) correct 29% (01:08) wrong based on 31 sessions
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
Intern
Status: Life begins at the End of your Comfort Zone
Joined: 31 Jul 2011
Posts: 47
Location: Tajikistan
Concentration: General Management, Technology
GPA: 3.86
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Kudos [?]: 23 [1] , given: 4

Re: In how many ways can a group of 3 people be selected [#permalink]  09 Nov 2012, 12:12
1
KUDOS
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]  10 Nov 2012, 03:48
Expert's post
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: $$C^3_7=35$$;

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Re: In how many ways can a group of 3 people be selected [#permalink]  12 Nov 2012, 00:45
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: $$C^3_7=35$$;

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]  28 Dec 2012, 04:05
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 = $$=\frac{7!}{2!5!} * \frac{5!}{1!4!} = 21 * 5 = 105$$

$$70 + 105 = 175$$

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Impossible is nothing to God.

Re: In how many ways can a group of 3 people be selected   [#permalink] 28 Dec 2012, 04:05
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