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# From a total of 5 boys and 4 girls, how many 4-person committees can

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Math Expert
Joined: 02 Sep 2009
Posts: 50004
From a total of 5 boys and 4 girls, how many 4-person committees can  [#permalink]

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26 Mar 2015, 04:21
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Difficulty:

5% (low)

Question Stats:

80% (00:59) correct 20% (01:14) wrong based on 131 sessions

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From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?

A. 16
B. 24
C. 60
D. 120
E. 240

Kudos for a correct solution.

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Director
Joined: 07 Aug 2011
Posts: 540
GMAT 1: 630 Q49 V27
Re: From a total of 5 boys and 4 girls, how many 4-person committees can  [#permalink]

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26 Mar 2015, 06:03
1
Bunuel wrote:
From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?

A. 16
B. 24
C. 60
D. 120
E. 240

Kudos for a correct solution.

$$C^2_5 * C^2_4 = 60$$
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Director
Joined: 21 May 2013
Posts: 651
Re: From a total of 5 boys and 4 girls, how many 4-person committees can  [#permalink]

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27 Mar 2015, 00:08
1
Bunuel wrote:
From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?

A. 16
B. 24
C. 60
D. 120
E. 240

Kudos for a correct solution.

No of 4 person committees that can be formed=5C2*4C2=60
Math Expert
Joined: 02 Sep 2009
Posts: 50004
Re: From a total of 5 boys and 4 girls, how many 4-person committees can  [#permalink]

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30 Mar 2015, 03:47
Bunuel wrote:
From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?

A. 16
B. 24
C. 60
D. 120
E. 240

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

Counting_and_Prob_Committees.png [ 26.21 KiB | Viewed 6246 times ]

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Posts: 99
From a total of 5 boys and 4 girls, how many 4-person committees can  [#permalink]

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30 Mar 2015, 09:30
From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?

A. 16
B. 24
C. 60
D. 120
E. 240

5 boys, 4 girls

((5!) / (2!3!)) x ((4!) / (2!2!)).

5! / 2!3! = 10
4! / 2!2! = 6

10 x 6 = 60.

C.
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Joined: 06 Nov 2014
Posts: 1883
Re: From a total of 5 boys and 4 girls, how many 4-person committees can  [#permalink]

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31 Mar 2015, 05:24
Bunuel wrote:
From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?

A. 16
B. 24
C. 60
D. 120
E. 240

Kudos for a correct solution.

2 boys can be selected from 5 boys in 5C2 ways = 10 ways
2 girls can be selected from 4 girls in 4C2 ways = 6 ways

Hence total number of ways = 10 * 6 = 60 ways.
Hence option (C).

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Re: From a total of 5 boys and 4 girls, how many 4-person committees can  [#permalink]

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17 Apr 2018, 16:27
Bunuel wrote:
From a total of 5 boys and 4 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?

A. 16
B. 24
C. 60
D. 120
E. 240

We can select 2 girls in 4C2 = (4 x 3)/2! = 6 ways.

We can select 2 boys in 5C2 = (5 x 4)/2! = 10 ways.

So the group can be formed in a total of 6 x 10 = 60 ways.

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Re: From a total of 5 boys and 4 girls, how many 4-person committees can &nbs [#permalink] 17 Apr 2018, 16:27
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