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CAT 2024 Slot 1 · Quant · Permutations, Combinations and Sets · hard

In how many ways can 5 boys and 3 girls be seated in a row such that no two girls sit together?

Single correct option

In how many ways can 5 boys and 3 girls be seated in a row such that no two girls sit together?
  1. A. 720
  2. B. 7200
  3. C. 12000
  4. D. 14400
Show answer and solution

Answer: (D) 14400

First seat the 5 boys in a row: 5! = 120 ways. This creates 6 gaps (including the two ends) in which the 3 girls can be placed so that no two girls are adjacent. Choose and arrange girls in 3 of these 6 gaps: 6×5×4 = 120 ways. Total arrangements = 120×120 = 14,400.
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Original question written in the CAT 2024 Slot 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake