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NDA 2023 Maths · Mathematics · Permutations and Combinations · easy

The number of distinct arrangements of the letters of the word BANANA is

Single correct option

The number of distinct arrangements of the letters of the word BANANA is
  1. A. 120120
  2. B. 720720
  3. C. 6060
  4. D. 3030
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Answer: (C) 6060

BANANA has 6 letters with A repeated 3 times and N repeated 2 times (B once). The number of arrangements is 6!3! 2!=72012=60\dfrac{6!}{3!\,2!}=\dfrac{720}{12}=60. Using 6!=7206!=720 ignores repetition, and dividing by 3! 2! 2!3!\,2!\,2! (double counting) gives 3030.
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake