Permutations And Combinations Ques 14
- 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: 14.(a)
Solution:
Formula:
Combinations under restrictions:
- 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 $
BETA
