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 selec

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 at most one boy, then the number of ways of selecting the team is [2016]

Smart Achievers · Accepted Answer

(1)

Either one boy will be selected or no boy will be selected.

Also out of four members one captain is to be selected.

$∴$ $Required number of ways = ({}^{4}C_{1} \times {}^{6}C_{3} + {}^{6}C_{4}) \times {}^{4}C_{1}$

$= (80 + 15) \times 4 = 380$

Solution

Q.
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 [2016]

1 380

2 320

3 260

4 95

Ans.
(1)

Either one boy will be selected or no boy will be selected.

Also out of four members one captain is to be selected.

$∴$ $Required number of ways = ({}^{4}C_{1} \times {}^{6}C_{3} + {}^{6}C_{4}) \times {}^{4}C_{1}$

$= (80 + 15) \times 4 = 380$

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