JEE Advance - Mathematics (2016 - Paper 1 Offline - No. 12)
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
380
320
260
95
Explanation
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 $={ }^4 C_1$ ways
Selection of 3 girls from 6 girls $={ }^6 \mathrm{C}_3$ ways
Selection of 4 girls from 6 girls $={ }^6 \mathrm{C}_4$ ways
$\therefore$ Total number of ways selecting the team $$ =\left({ }^4 \mathrm{C}_1 \cdot{ }^6 \mathrm{C}_3+{ }^6 \mathrm{C}_4\right) \times 4 $$
(since, among any of the selection we have 4 choice to select captain)
$$ \begin{aligned} \therefore \text { Total number of ways } & =(4 \times 20+15) \times 4 \\\\ & =380 \end{aligned} $$
$\therefore$ We can have one boy and three girls in team or all four girls. So, selection of 1 boy from 4 boys $={ }^4 C_1$ ways
Selection of 3 girls from 6 girls $={ }^6 \mathrm{C}_3$ ways
Selection of 4 girls from 6 girls $={ }^6 \mathrm{C}_4$ ways
$\therefore$ Total number of ways selecting the team $$ =\left({ }^4 \mathrm{C}_1 \cdot{ }^6 \mathrm{C}_3+{ }^6 \mathrm{C}_4\right) \times 4 $$
(since, among any of the selection we have 4 choice to select captain)
$$ \begin{aligned} \therefore \text { Total number of ways } & =(4 \times 20+15) \times 4 \\\\ & =380 \end{aligned} $$
Comments (0)
