Question

A debate club consists of $6$ girls and $4$ boys. A team of $4$ members is said 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 be include at most one boy, then 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

Given that there is atmost one boy in the group of $4$.

Therefore the selection of $4$ members team has $2$ possibilities. They are $1)$ all $4$ members are girls $,$ $2)$ $3$ girls and $1$ boy

From first possibility we can select $4$ members in ${{}^{6}C}_4=15$ ways

From the second possibility we can select $4$ members in ${{}^{6}C}_3\times {{}^{4}C}_1=80$ways

Therefore we can select $4$ members in $95$ ways

Captain can be selected from the group of $4$ members in ${{}^{4}C}_1=4$ ways

Therefore, the number of ways of selecting team of $4$ members including selection of captain is $95\times 4=380$