Permutations and Combinations · Class 11 · CBSE · Science Mathematics

How many distinct arrangements can be made using all the letters of the word BANANA?

Practice question from Permutations and Combinations (Class 11 · CBSE · Science Mathematics), with the correct answer and a step-by-step solution.

easy · MCQ · Q-BB8123

How many distinct arrangements can be made using all the letters of the word BANANA?

  1. A.20
  2. B.60Correct answer
  3. C.120
  4. D.360

Solution

The word BANANA has 6 letters, with A repeated 3 times and N repeated 2 times. Therefore, the number of distinct arrangements is 6!3!2!=60\frac{6!}{3!2!}=60.

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