Verified Solution • 2025–26 Session moderate

QJEEAdv16Ma24fc: JEE Advanced 2016 Mathematics - Class 11 JEEAdv16Ma24fc Solution: A debate club consists of 6 girls and 4 boys. A team of 4…

A debate club consists of 6 girls and 4 boys. A team of 4 members is to be select 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

Multiple Choice Options

  • A 380
  • B 320
  • C 260
  • D 95

Step-by-Step Verified Solution

We have 6 girls and 4 boys in the club and we have to select team of 4 members in which one is captain and at most one boy.

∴\therefore We can have one boy and three girls in team or all four girls. So, selection of 1 boy from 4 boys =4C1={ }^4 C_1 ways

Selection of 3 girls from 6 girls =6C3={ }^6 \mathrm{C}_3 ways

Selection of 4 girls from 6 girls =6C4={ }^6 \mathrm{C}_4 ways

∴\therefore Total number of ways selecting the team =(4C1⋅6C3+6C4)×4=\left({ }^4 \mathrm{C}_1 \cdot{ }^6 \mathrm{C}_3+{ }^6 \mathrm{C}_4\right) \times 4

(since, among any of the selection we have 4 choice to select captain)

∴ Total number of ways amp;=(4×20+15)×4amp;=380\begin{aligned}\therefore \text { Total number of ways } & =(4 \times 20+15) \times 4 \\\\& =380\end{aligned}

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