How Many Distinct Arrangements of BALLOON Are There?

Exact result

1,260

For item-group counts 2, 2, 1, 1, 1, the number of distinct arrangements is 1,260.

BALLOON has counts 2,2,1,1,1 because L repeats twice, O repeats twice, and B, A, and N are singles. The repeated pairs are handled by dividing out the duplicate arrangements they create.

Worked steps

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Inputs: item-group counts = 2, 2, 1, 1, 1
Formula: T! / (n1! n2! n3! ...)
Substitute: 7! / (2! 2! 1! 1! 1!)
Steps: start with 5,040 and divide by 2! = 2, 2! = 2, 1! = 1, 1! = 1, 1! = 1
Result: For item-group counts 2, 2, 1, 1, 1, the number of distinct arrangements is 1,260.

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BALLOON has counts 2,2,1,1,1 because L repeats twice, O repeats twice, and B, A, and N are singles. The repeated pairs are handled by dividing out the duplicate arrangements they create.

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 BALLOON are there?

1,260

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