How Many Distinct Arrangements of BANANA Are There?

Exact result

60

For item-group counts 3, 2, 1, the number of distinct arrangements is 60.

BANANA has counts 3,2,1 because A appears 3 times, N appears 2 times, and B appears once. The total starts from 6! and then removes duplicate swaps of the repeated letters.

Worked steps

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Inputs: item-group counts = 3, 2, 1
Formula: T! / (n1! n2! n3! ...)
Substitute: 6! / (3! 2! 1!)
Steps: start with 720 and divide by 3! = 6, 2! = 2, 1! = 1
Result: For item-group counts 3, 2, 1, the number of distinct arrangements is 60.

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BANANA has counts 3,2,1 because A appears 3 times, N appears 2 times, and B appears once. The total starts from 6! and then removes duplicate swaps of the repeated letters.

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 BANANA are there?

60

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