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CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations

How many distinct arrangements can be made from all the letters of the word 'ACCOUNTS'?

There are 20160 distinct arrangements. The word has 8 letters with the letter C occurring twice, so the total 8! = 40320 must be divided by 2! to remove duplicate arrangements, giving 20160.

  1. A20160Correct
  2. B40320
  3. C10080
  4. D5040

Explanation

ACCOUNTS has 8 letters in which C appears twice. The other letters are distinct (A, O, U, N, T, S). Arrangements = 8!/2! = 40320/2 = 20160. The option 40320 ignores the repeated C.

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