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Around the World in 80 Questions (Day 8): If there are 5 girls and 4

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Bunuel
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Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] Around the World in 80 Questions (Day 8): If there are 5 girls and 4   26 Jul 2023, 08:00
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37% (01:46) correct 63% (01:31) wrong based on 209 sessions
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If there are 5 girls and 4 boys at a school ball, how many ways can 3 boy-girl dance pairs be formed?

A. 15
B. 20
C. 40
D. 240
E. 1440


 


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D
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] Around the World in 80 Questions (Day 8): If there are 5 girls and 4   26 Jul 2023, 08:15
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Asked: If there are 5 girls and 4 boys at a school ball, how many ways can 3 boy-girl dance pairs be formed?

The number of ways to select 3 girls out of 5 girls = 5C3 = 10
The number of ways to select 3 boys out of 4 boys = 4C3 = 4
The number of ways to select 3 boy-girl pairs out of 3 boys and 3 girls = 3! = 6
The number of ways 3 boy-girl dance pairs be formed = 5C3*4C3 * 3! = 10*4*6 = 240

IMO D
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] Around the World in 80 Questions (Day 8): If there are 5 girls and 4   26 Jul 2023, 08:42
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Bunuel wrote:
If there are 5 girls and 4 boys at a school ball, how many ways can 3 boy-girl dance pairs be formed?

A. 15
B. 20
C. 40
D. 240
E. 1440


 


This question was provided by GMAT Club
for the Around the World in 80 Questions

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3 girls can be chosen in 5c3 ways
3 boys can be chosen in 4c3 ways
3 boys and 3 girls can be paired in 3*2*1 = 6 ways, similar to 3 seats and 3 people.

Multiplying all together, 10*4*6 = 240
D is the right choice.
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] Around the World in 80 Questions (Day 8): If there are 5 girls and 4   26 Jul 2023, 08:51
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Bunuel wrote:
If there are 5 girls and 4 boys at a school ball, how many ways can 3 boy-girl dance pairs be formed?

A. 15
B. 20
C. 40
D. 240
E. 1440


 


This question was provided by GMAT Club
for the Around the World in 80 Questions

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Pair 1 : Select one girl out of 5 girls * Select one boy out of 4 boys = 5 * 4

Pair 2 : Select one girl out of 4 girls * Select one boy out of 4 boys = 4 * 3

Pair 3 : Select one girl out of 3 girls * Select one boy out of 2 boys = 3 * 2

However we need to divide by 3! as we have taken the order into account.

Ex B1G1 B2G2 B3G3 is same as B3G3 B2G2 B1G1 etc.

(5*4*4*3*3*2)/3! = 5*4*4*3 = 20 * 12 = 240

IMO D
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] Around the World in 80 Questions (Day 8): If there are 5 girls and 4   26 Jul 2023, 09:14
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select 3 -3 pairs

5C3 x 4C3

Let girls be G1 G2 G3
Lets arrange boys in front of these Girls (3!)

5C3 x 4C3x3!=10*4*6=240
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] Around the World in 80 Questions (Day 8): If there are 5 girls and 4   26 Jul 2023, 21:23
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Bunuel wrote:
If there are 5 girls and 4 boys at a school ball, how many ways can 3 boy-girl dance pairs be formed?

A. 15
B. 20
C. 40
D. 240
E. 1440
 


This question was provided by GMAT Club
for the Around the World in 80 Questions

Win over $20,000 in prizes: Courses, Tests & more

 



We need 3 pairs of 1 boy and 1 girl
We first select 3 boys - 4C3 = 4 ways
We also select 3 girls - 5C3 = 10 ways
Thus, total number of ways of selecting = 4 * 10 = 40

Now, each boy has to be paired with a girl.
For the first boy, there are 3 options, for the second boy there are 2 options and for the third boy, there is one option
Thus, total pairings possible = 3*2*1 = 3! = 6

Thus, total number of ways = 40 * 6 = 240
Answer D
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink]
26 Jul 2023, 21:23
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Bunuel
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