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CAT 2023 Slot 2 · Quant · Permutations, Combinations and Sets · hard

In how many ways can the letters of the word 'MANAGE' be arranged so that the two A's are never together?

Single correct option

In how many ways can the letters of the word 'MANAGE' be arranged so that the two A's are never together?
  1. A. 120
  2. B. 180
  3. C. 240
  4. D. 300
Show answer and solution

Answer: (C) 240

MANAGE has 6 letters with A repeated twice, so total arrangements = 6!/2! = 360. Treating the two A's as a single block gives 5 units, arranged in 5! = 120 ways (all together). Arrangements with the A's not together = 360 − 120 = 240.
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Original question written in the CAT 2023 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake