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Bunuel
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From a total of 5 boys and 4 girls, how many 4-person committees can 26 Mar 2015, 04:21
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C
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81% (00:58) correct 19% (01:18) wrong based on 426 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

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C
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From a total of 5 boys and 4 girls, how many 4-person committees can 26 Mar 2015, 06:03
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Bunuel
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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Answer C

\(C^2_5 * C^2_4 = 60\)
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From a total of 5 boys and 4 girls, how many 4-person committees can 27 Mar 2015, 00:08
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Bunuel
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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Answer=C=60

No of 4 person committees that can be formed=5C2*4C2=60
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From a total of 5 boys and 4 girls, how many 4-person committees can 30 Mar 2015, 03:47
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Bunuel
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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MAGOOSH OFFICIAL SOLUTION:
Attachment:
Counting_and_Prob_Committees.png
Counting_and_Prob_Committees.png [ 26.21 KiB | Viewed 21266 times ]
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From a total of 5 boys and 4 girls, how many 4-person committees can 30 Mar 2015, 09:30
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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


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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From a total of 5 boys and 4 girls, how many 4-person committees can 31 Mar 2015, 05:24
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Bunuel
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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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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From a total of 5 boys and 4 girls, how many 4-person committees can 17 Apr 2018, 16:27
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Bunuel
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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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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From a total of 5 boys and 4 girls, how many 4-person committees can 11 Feb 2020, 18:45
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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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From a total of 5 boys and 4 girls, how many 4-person committees can 01 Aug 2020, 10:42
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jfranciscocuencag
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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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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From a total of 5 boys and 4 girls, how many 4-person committees can 28 Jun 2025, 18:20
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