How Many Distinct Arrangements of MISSISSIPPI Are There?

Exact result

34,650

For item-group counts 4, 4, 2, 1, the number of distinct arrangements is 34,650.

MISSISSIPPI has counts 4,4,2,1 because I and S each appear 4 times, P appears 2 times, and M appears once. Dividing out the repeated-letter swaps leaves only the unique visible arrangements.

Worked steps

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Inputs: item-group counts = 4, 4, 2, 1
Formula: T! / (n1! n2! n3! ...)
Substitute: 11! / (4! 4! 2! 1!)
Steps: start with 39,916,800 and divide by 4! = 24, 4! = 24, 2! = 2, 1! = 1
Result: For item-group counts 4, 4, 2, 1, the number of distinct arrangements is 34,650.

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MISSISSIPPI has counts 4,4,2,1 because I and S each appear 4 times, P appears 2 times, and M appears once. Dividing out the repeated-letter swaps leaves only the unique visible arrangements.

Item-group counts Use this when some items are already identical before arranging. Enter one count per distinct type, separated by commas. Example: APPLE -> 2,1,1,1. Optional item to count entry Enter a word, number string, or emoji string to auto-fill item-group counts. Item examples Selecting an example fills the optional entry box and then auto-fills item-group counts.

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Calculation work

How many distinct arrangements of the letters in MISSISSIPPI are there?

34,650

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