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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] New post   26 Jul 2023, 08:00
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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] New post   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] New post   26 Jul 2023, 08:21
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the number of ways to choose 3 boys out of 4 is C(4, 3) = 4! / [3!(4-3)!] = 4.

Next, we need to determine how many ways we can choose 3 girls out of 5. Again, this is a combination problem. So, the number of ways to choose 3 girls out of 5 is C(5, 3) = 5! / [3!(5-3)!] = 10.

Now, for each of the 3 boy-girl pairs, there are 3! = 3*2*1 = 6 ways to arrange them.

So, the total number of ways to form 3 boy-girl dance pairs is 4 (ways to choose boys) * 10 (ways to choose girls) * 6 (ways to arrange the pairs) = 240.

D is the answer
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] New post   26 Jul 2023, 08:29
ways to select 3 girls from 5 which can be random
5*4*3 ; 60
ways to select 3 boys from 4
4*3*2 ; 24
60*24 ; 1440 total ways to form 3 boy-girl group
OPTION E
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


 


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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] New post   26 Jul 2023, 08:36
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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


 


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for the Around the World in 80 Questions

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First, we choose 3 boys out of 4, which can be done in 4C3 ways.
Then, we choose 3 girls out of 5, which can be done in 5C3 ways.
Finally, the 3 chosen boys and 3 chosen girls can pair up in 3! ways.
So, the total number of ways is 4C3 * 5C3 * 3! = 4 * 10 * 6 = 240.
Therefore, the correct answer is D.
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] New post   26 Jul 2023, 08:38
The answer is C= 40
The number of ways to choose 3 boys from 4 is given by the combination formula (4 choose 3):
Number of ways to choose 3 boys = C(4, 3) = 4
The number of ways to choose 3 girls from 5 is given by the combination formula (5 choose 3):
Number of ways to choose 3 girls = C(5, 3) = 10
To find the total number of ways to form 3 boy-girl dance pairs, we multiply the number of ways to choose 3 boys and the number of ways to choose 3 girls:
Total number of ways = Number of ways to choose 3 boys × Number of ways to choose 3 girls
Total number of ways = 4 × 10 = 40
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] New post   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] New post   26 Jul 2023, 08:45
My Answer: C

5C3 * 4C3 = 40 ( number of ways 3 girls can be chosen * number of ways 3 boys can be chosen)
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] New post   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


 


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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] New post   26 Jul 2023, 08:57
If there are 5 girls and 4 boys at a school ball, how many ways can 3 boy-girl dance pairs be formed?

3 boy-girl dance pairs, where
(5 girls can be selected * 4 boys can be selected) *(4 girls can be selected * 3 boys can be selected) * (3 girls can be selected * 2 boys can be selected)
(5*4)*(4*3)*(3*2)= (20)(12)(6)= 240*6= (250-10)*6= 1500-60=1440

A. 15
B. 20
C. 40
D. 240
E. 1440
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] New post   26 Jul 2023, 09:02
Quote:
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

Girls= 5 & boys = 4
we need to select 3 girls out of 5 and 3 boys out of 4.
#ways = 5C3*4C3 = 10*4 = 40.

OA: C
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] New post   26 Jul 2023, 09:06
To form 3 boy-girl dance pairs, we need to select 3 boys out of 4 and 3 girls out of 5. The number of ways to do this is 4C3 * 5C3 = 4 * 10 = 40. Therefore, there are 40 ways to form 3 boy-girl dance pairs.

Answer is C
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] New post   26 Jul 2023, 09:09
No of girls : 5
No of boys : 4
No of boy-girl groups to be formed= 3

No of ways in which first group can be formed = no of ways 1 girl can be selected from 5 girls * no of ways 1 boy can be selected from 4 boys = 5C1 * 4C1=5*4=20
similarly ,
No of ways in which second group can be formed from the remaining boys and girls = 4C1*3C1=4*3=12
No of ways in which third group can be formed from the remaining boys and girls = 3C1*2C1=3*2=6

Total number of ways in which 3 groups can be formed = 20 * 12 * 6 = 1440

Answer : E = 1440
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] New post   26 Jul 2023, 09:10
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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

Solution:
Firstly, we need to select 3 boys from 4 and 3 girls from 4. No. of ways for doing it=5C3 * 4C3 = 40
Now, we need to arrange them in pairs. Selected G1 has 3 options (B1, B2, B3). G2 will have 2 options (The ones left after pairing with G1). G3 will have only 1 option(the remaining boy).
So, total no ways to arrange them= 3*2*1=6.
So, total no. of ways in which 3 boy-girl dance pairs be formed = 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] New post   26 Jul 2023, 09:11
If there are 5 girls and 4 boys at a school ball, how many ways can 3 boy-girl dance pairs be formed?
choose 3 boys from 4 hence we get 4C3 which is 4 ways
then choose 3 girls from 5 girls 5C3 which is 10 ways
Hence we have 4*10 = 40 ways

A. 15
B. 20
C. 40
D. 240
E. 1440
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] New post   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] New post   26 Jul 2023, 09:14
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Select 3 boys = 4C3 = 4
Select 3 girls = 5C3 = 5*4*3!/ 3! * 2 = 10

Selection of boys and girls = 40 ways
# ways to make 3 pairs = 40 * 3! = 40*3*2 = 240 [D]
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] New post   26 Jul 2023, 09:18
The number of ways to choose 3 boys from 4 is given by the combination formula "C(4, 3)", which can be calculated as:

C(4, 3) = 4! / (3! * (4-3)!) = 4

Similarly, the number of ways to choose 3 girls from 5 is given by the combination formula "C(5, 3)", which can be calculated as:

C(5, 3) = 5! / (3! * (5-3)!) = 10

Now, we have 4 ways to choose 3 boys and 10 ways to choose 3 girls. To form boy-girl pairs, we multiply these two numbers together:

Number of ways to form boy-girl pairs = 4 * 10 = 40

So, there are 40 different ways to form 3 boy-girl dance pairs at the school ball.
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] New post   26 Jul 2023, 09:22
number of ways to choose 3 boys from 4 is C(4, 3) = 4,

number of ways to choose 3 girls from 5 is C(5, 3) = 10.

total number of ways to form the pairs, you multiply these two combinations: 4 boys * 10 girls = 40

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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink] New post   26 Jul 2023, 09:28
IMO B

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

Let's say we select Girl 1 (G1).. Then the number of ways we can select 3 boys from 4 would be 4C3 ie 4

Same with G2, G3, G4 and G5

In each case, we have 4 possible cases.. Hence, 4*5 = 20 cases. Hence B
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Re: Around the World in 80 Questions (Day 8): If there are 5 girls and 4 [#permalink]
26 Jul 2023, 09:28
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