A debate club consists of 6 girls and 4 boys. A team of 4 members is to be selected from this club including the selection of a captain (from among these 4 members) for the team. If the team has to include at most one boy, then the number of ways of selecting the team is
- (A)380✓ Correct
- (B)320
- (C)260
- (D)95
Answer: (A)
Solution
"At most one boy" means either 0 boys or 1 boy.
Case 1: 1 boy, 3 girls
Select 1 boy from 4:
Select 3 girls from 6:
Select captain from these 4 members:
Total:
Case 2: 0 boys, 4 girls
Select 4 girls from 6:
Select captain from these 4 members:
Total:
Total ways = .
Case 1: 1 boy, 3 girls
Select 1 boy from 4:
Select 3 girls from 6:
Select captain from these 4 members:
Total:
Case 2: 0 boys, 4 girls
Select 4 girls from 6:
Select captain from these 4 members:
Total:
Total ways = .
JEE Advanced · 2016 · 22 May 2016 · Paper 1 · Single correct option