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CA Foundation · Quantitative Aptitude · Permutations and Combinations

How many distinct arrangements of the letters of the word 'BANANA' are there in which the first letter is B?

The answer is 10. With B fixed first, the remaining five letters A, A, A, N, N can be arranged in 5!/(3! × 2!) = 10 ways. The option 60 is the unrestricted total for BANANA.

  1. A10Correct
  2. B20
  3. C60
  4. D6

Explanation

Fix B in the first place. The remaining letters A, A, A, N, N occupy 5 positions. Arrangements = 5!/(3! 2!) = 120/12 = 10. The option 60 is the total number of arrangements of BANANA without the restriction.

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