Question

A debate club consists of $6$ girls and $4$ boys. A team of $4$ members is to be selected from this club including a selection of a captain (from among these four 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. $95$

Answer 1

The correct option is A $380$

Case $1$: $0$ boy is included
Selecting $4$ girls from $6$ girls = ${}^6{C}_4$
Selecting $1$ captain from the selected members = ${}^4{C}_1$

Total for case $1$ = ${}^6{C}_4\times {}^4{C}_1=60$

Case $2$: $1$ boy is included
Selecting $3$ girls and $1$ boy from given members $={}^6{C}_3\times {}^4{C}_1$
Selecting $1$ captain from the selected members = ${}^4{C}_1$

Total for case $2$$={}^6{C}_3\times {}^4{C}_1\times {}^4{C}_1=320$

Total $=60+320=380$