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) 44389I had been asked this question in an international level competition.My doubt is from Fundamental Principle of Counting in section Counting of Discrete Mathematics

A head boy, two deputy head boys, a head girl and 3 deputy head girls

1.	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) 44389I had been asked this question in an international level competition.My doubt is from Fundamental Principle of Counting in section Counting of Discrete Mathematics
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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