Permutations and Combinations 2 Question 10
10. 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 atmost one boy, the number of ways of selecting the team is
(2016 Adv.)
(a) 380
(b) 320
(c) 260
(d) 95
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Answer:
Correct Answer: 10. (a)
Solution:
- We have, 6 girls and 4 boys. To select 4 members (atmost one boy)
i.e. ( 1 boy and 3 girls) or (4 girls) $={ }^{6} C _3{ }^{4} C _1+{ }^{6} C _4$
Now, selection of captain from 4 members $={ }^{4} C _1$
$\therefore$ Number of ways to select 4 members (including the selection of a captain, from these 4 members) $=\left({ }^{6} C _3 \cdot{ }^{4} C _1+{ }^{6} C _4\right){ }^{4} C _1$
$ =(20 \times 4+15) \times 4=380 $
