Question

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 atmost one boy, the number of ways of selecting the team is ?

• A. 380
• B. 320
• C. 260
• D. 95

Answer 1

The correct option is A 380

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 (including the selection of a captain, from these 4 members)
${(}^6{C}_3{.}^4{C}_1{+}^6{C}_4{)}^4{C}_1=(20\times 4+15)\times 4=380$