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CAT 2020 Slot 3 · Quant · Permutations, Combinations and Sets · hard

In how many ways can the letters of the word BANANA be arranged so that no two A's are adjacent?

Single correct option

In how many ways can the letters of the word BANANA be arranged so that no two A's are adjacent?
  1. A. 12
  2. B. 18
  3. C. 24
  4. D. 36
Show answer and solution

Answer: (A) 12

Place the non-A letters first: B, N, N can be arranged in 3!/2! = 3 ways.

They create 4 gaps ( _ X _ X _ X _ ). The three identical A's must go into 3 different gaps: C(4, 3) = 4 ways.

Total = 3 × 4 = 12.

Tip: 'No two alike together' → arrange the others, then choose gaps.
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Original question written in the CAT 2020 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