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From a total of 5 boys and 4 girls, how many 4-person committees can
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Bunuel
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From a total of 5 boys and 4 girls, how many 4-person committees can [#permalink] New post  26 Mar 2015, 03:21
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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

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Lucky2783
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Re: From a total of 5 boys and 4 girls, how many 4-person committees can [#permalink] New post  26 Mar 2015, 05:03
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.


Answer C

\(C^2_5 * C^2_4 = 60\)
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KS15
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Re: From a total of 5 boys and 4 girls, how many 4-person committees can [#permalink] New post  26 Mar 2015, 23:08
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.


Answer=C=60

No of 4 person committees that can be formed=5C2*4C2=60
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Bunuel
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Re: From a total of 5 boys and 4 girls, how many 4-person committees can [#permalink] New post  30 Mar 2015, 02:47
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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
Counting_and_Prob_Committees.png [ 26.21 KiB | Viewed 11376 times ]

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DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

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SavageBrother
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From a total of 5 boys and 4 girls, how many 4-person committees can [#permalink] New post  30 Mar 2015, 08:30
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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OptimusPrepJanielle
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Re: From a total of 5 boys and 4 girls, how many 4-person committees can [#permalink] New post  31 Mar 2015, 04:24
Expert Reply
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] New post  17 Apr 2018, 15:27
1
Expert Reply
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.

Answer: C
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jfranciscocuencag
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Re: From a total of 5 boys and 4 girls, how many 4-person committees can [#permalink] New post  11 Feb 2020, 17:45
Why is it wrong to do it like:

5*4 for boys and 4*3 of girls?

Giving 240?

Kind regards!
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CMIREK
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Re: From a total of 5 boys and 4 girls, how many 4-person committees can [#permalink] New post  01 Aug 2020, 09:42
jfranciscocuencag wrote:
Why is it wrong to do it like:

5*4 for boys and 4*3 of girls?

Giving 240?

Kind regards!


Since order doesn't matter, you would still need to get rid of duplicate groups for both boys and girls. In 5*4, you are duplicating so you would need to divide by 2, and the same for 4*3 in girls. Or you can divide 240 by 4 and get the correct answer of 60.
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