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A head boy, two deputy head boys, a head girl and 3 deputy head girls must be chosen out of a student council consisting of 14 girls and 16 boys. In how many ways can they are chosen?

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A head boy, two deputy head boys, a head girl and 3 deputy head girls must be chosen out of a student council consisting of 14 girls and 16 boys. In how many ways can they are chosen?

(a) 98072

(b) 27384

(c) 36428

(d) 44389

I had been asked this question in an international level competition.

My doubt is from Fundamental Principle of Counting in section Counting of Discrete Mathematics

1 Answer

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Best answer
Right option is (b) 27384

Explanation: There are 16 × 15 × 14 + 14 × 13 × 12 × 11 = 27384 ways to choose from a student council.

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