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JEE Advanced 2016Paper 1
Exam
JEE Advanced
Year
2016
Paper
Paper 1
Subject
Mathematics
Chapter
Permutation and Combination

JEE Advanced 2016 · Paper 1 · Mathematics · Permutation and Combination

A debate club consists of 6 girls and 4 boys. A team of 4 members...

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

Options

  1. A380
  2. B320
  3. C260
  4. D95

Correct answer

A. 380

Step-by-step solution

There are 2 cases-

i. All the 4 are girls

ii. 3 girls and 1 boy

So the answer is

(6C4+6C3.4C1).4C1=380\left({}^{6}{C}_{4} + {}^{6}{C}_{3} . {}^{4}{C}_{1}\right) . {}^{4}{C}_{1} = 380 (4C1={}^{4}{C}_{1} = No. of ways of selecting captain)

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