A debate club consist 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 -

Question

A debate club consist 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

Tardigrade Admin · Accepted Answer

Total No. of ways =( 4 C 0 × 6 C 4+ 4 C 1 × 6 C 3) × 4 C 1 =(15+80) × 4 =380

Q. A debate club consist 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 -

380

320

260

95

Total No. of ways
$= (^{4} C_{0} \times^{6} C_{4} +^{4} C_{1} \times^{6} C_{3}) \times^{4} C_{1}$
$= (15 + 80) \times 4$
$= 380$

Q. A debate club consist 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 -

380

320

260

95

Total No. of ways =(4C0​×6C4​+4C1​×6C3​)×4C1​ =(15+80)×4 =380

Q. A debate club consist 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 -

Total No. of ways
$= (^{4} C_{0} \times^{6} C_{4} +^{4} C_{1} \times^{6} C_{3}) \times^{4} C_{1}$
$= (15 + 80) \times 4$
$= 380$