Permutations

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The number of permutations of the word 'MISSISSIPPI' is

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34650

33600

39600

36960

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About This Question

Subject: mathematics
Chapter: permutations and combinations
Topic: permutations
Difficulty: Medium
Year: 2025

Solution

Correct Answer:

34650

Count Total Letters: 'MISSISSIPPI' has 11 letters.
Identify Repetitions:
- M: 1 time
- I: 4 times
- S: 4 times
- P: 2 times
Formula for Permutations of Multisets: $\frac{n !}{p ! q ! r ! \dots}$ , where $p, q, r$ are the counts of identical objects.
Substitution:
- $\frac{11 !}{1 ! \times 4 ! \times 4 ! \times 2 !}$
Calculation:
- $\frac{39 , 916 , 800}{1 \times 24 \times 24 \times 2} = \frac{39 , 916 , 800}{1 , 152} = 34, 650$ .
Result: 34,650 permutations.

This medium difficulty mathematics question is from the chapter permutations and combinations, covering the topic of permutations. It appeared in the 2025 exam.

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