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NDA 2020 Maths · Mathematics · Permutations and Combinations · hard

In how many ways can 5 boys and 3 girls stand in a row so that no two girls are adjacent?

Single correct option

In how many ways can 5 boys and 3 girls stand in a row so that no two girls are adjacent?
  1. A. 720
  2. B. 4320
  3. C. 40320
  4. D. 14400
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Answer: (D) 14400

Arrange the boys first: 5!=1205!=120 ways. This leaves 6 gaps, and the 3 girls take 3 distinct gaps in (63)⋅3!=120\binom63\cdot3!=120 ways. Total 120×120=14400120\times120=14400. The number 8!=403208!=40320 ignores the condition.
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Original question written in the NDA 2020 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake