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

Question

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

Kinshook · Answer

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

charlie07 · Answer

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.

missionmba2025 · Answer

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

Oppenheimer1945 · Answer

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

sujoykrdatta · Answer

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

bumpbot · Answer

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

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

Prep Toolkit

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