Permutations

Question

The number of permutations of the word 'MISSISSIPPI' is

RankGuru · Accepted Answer

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

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