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A debate club consists of 6 girls and 4 ...

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

B

320

C

260

D

95

Text Solution

Verified by Experts

The correct Answer is:
A
we have, 6 girls and 4 boys. To select 4 members (atmost one boy)
i.e. (1 boy and 3 girls) or (4 girls) `= ""^(6)C_(3).""^(4)C_(1) + ""^(6)C_(4) " "..(i)`
Now, selection of captain from 4 members `= ""^(4)C_(1) " "(ii)`
`therefore` Number of ways to select 4 members (including the selection of a captain, from these 4 members)
`= (""^(6)C_(3)*""^(4)C_(1) + ""^(6)C_(4)) ""^(4)C_(1)`
`= (20 xx 4 + 15) xx 4 = 380`
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