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CA Foundation · Quantitative Aptitude · Permutations and Combinations

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

The answer is 34650. MISSISSIPPI has 11 letters with I four times, S four times and P twice, so the arrangements are 11! divided by 4!, 4! and 2!, which equals 34650. Dividing removes the duplicate orderings of identical letters.

  1. A34650Correct
  2. B39916800
  3. C69300
  4. D8316000

Explanation

MISSISSIPPI has 11 letters: I appears 4 times, S 4 times, P 2 times, M once. Arrangements = 11!/(4! 4! 2!) = 39916800/(24×24×2) = 39916800/1152 = 34650. The option 39916800 is 11! and ignores the repeated letters.

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