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

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

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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

Kudos for a correct solution.

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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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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

\(C^2_5 * C^2_4 = 60\)
Director
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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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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
Math Expert
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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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New post 30 Mar 2015, 02:47
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
Counting_and_Prob_Committees.png [ 26.21 KiB | Viewed 7236 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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From a total of 5 boys and 4 girls, how many 4-person committees can  [#permalink]

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

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New post 31 Mar 2015, 04:24
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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New post 17 Apr 2018, 15:27
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.

Answer: C
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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, 15:27
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