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18 May 2026, 19:00
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
70% (02:25) correct
30%
(02:33)
wrong
based on 202
sessions
History
Date
Time
Result
Not Attempted Yet
A team of 3 boys and 4 girls is to be made from a team of 5 boys and 6 girls. Sam, who is one of the boys, is selected only if his sister, Eloise, who is one of the girls, is also selected. How many different teams are possible?
A. 75
B. 100
C. 120
D. 150
E. 200
A. 75
B. 100
C. 120
D. 150
E. 200
ankushsambare
Joined: 13 Jun 2022
Last visit: 06 Sep 2026
Posts: 313
Given Kudos: 230
Location: India
Schools: ISB '27 Wharton '26 INSEAD Aug '26
GPA: 2.4
Products:
18 May 2026, 20:37
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We need a team of:
Sam is selected only if Eloise is also selected.
Start with total teams without restriction:
Choose 3 boys:
5C3 = 10
Choose 4 girls:
6C4 = 15
Total:
10 × 15 = 150
Now subtract invalid teams:
Sam selected but Eloise not selected.
If Sam is included:
Choose remaining 2 boys from other 4:
4C2 = 6
Eloise excluded, so choose 4 girls from remaining 5:
5C4 = 5
Invalid teams:
6 × 5 = 30
Valid teams:
150 − 30 = 120
Answer: C) 120
- 3 boys from 5 boys
- 4 girls from 6 girls
Sam is selected only if Eloise is also selected.
Start with total teams without restriction:
Choose 3 boys:
5C3 = 10
Choose 4 girls:
6C4 = 15
Total:
10 × 15 = 150
Now subtract invalid teams:
Sam selected but Eloise not selected.
If Sam is included:
Choose remaining 2 boys from other 4:
4C2 = 6
Eloise excluded, so choose 4 girls from remaining 5:
5C4 = 5
Invalid teams:
6 × 5 = 30
Valid teams:
150 − 30 = 120
Answer: C) 120
23 May 2026, 04:00
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ExpertsGlobal5
C is the correct answer choice.
Video explanation:
04 Jul 2026, 10:05
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What is wrong with below approach? I'm getting the answer as 80.
We have two scenarios when Sam and elois are included and when they are not included
Not Included:
Then we have 4 boys total of which 3 are needed and 5 girls total of which 4 are needed:
count = 4C3*5C4
= 20
Included:
we already include sam and elois now, so reduce required people by1
Then we have still have 4 boys of which. 2 are needed and 5 girls of which 3 are needed:
count= 4C2*5C3
=60
Total count = 20+60
=80
Please help me if I did some mistake here
We have two scenarios when Sam and elois are included and when they are not included
Not Included:
Then we have 4 boys total of which 3 are needed and 5 girls total of which 4 are needed:
count = 4C3*5C4
= 20
Included:
we already include sam and elois now, so reduce required people by1
Then we have still have 4 boys of which. 2 are needed and 5 girls of which 3 are needed:
count= 4C2*5C3
=60
Total count = 20+60
=80
Please help me if I did some mistake here
