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CAT 2024 Slot 3 · Quant · Permutations, Combinations and Sets · medium

In how many ways can 5 men and 3 women be seated in a row such that no two women sit next to each other?

Single correct option

In how many ways can 5 men and 3 women be seated in a row such that no two women sit next to each other?
  1. A. 7200
  2. B. 10800
  3. C. 14400
  4. D. 20160
Show answer and solution

Answer: (C) 14400

First arrange the 5 men: 5! = 120 ways. This creates 6 gaps (including the two ends) in which the 3 women can be placed so no two are adjacent: choose and arrange 3 of these 6 gaps for the women = P(6,3) = 6×5×4 = 120 ways. Total = 120 × 120 = 14400.
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Original question written in the CAT 2024 Slot 3 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake