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CAT 2017 Slot 1 · Quant · Permutations, Combinations and Sets · medium

In how many distinct ways can the letters of the word BANANA be arranged so that the two N's are not next to each other?

Single correct option

In how many distinct ways can the letters of the word BANANA be arranged so that the two N's are not next to each other?
  1. A. 20
  2. B. 36
  3. C. 60
  4. D. 40
Show answer and solution

Answer: (D) 40

Total arrangements of BANANA (3 A's, 2 N's, 1 B) = 6!/(3! · 2!) = 60.

Arrangements with the two N's together: treat NN as one block → B, A, A, A, [NN] → 5!/3! = 20.

Required = 60 − 20 = 40.

Alternative (gap method): Arrange B, A, A, A in 4!/3! = 4 ways; this creates 5 gaps; choose 2 gaps for the identical N's: C(5, 2) = 10. Total = 4 × 10 = 40.
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Original question written in the CAT 2017 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