How many distinct arrangements of the letters in the word LETTER are there?

Exact result

180

For item-group counts 2, 2, 1, 1, the number of distinct arrangements is 180.

LETTER has counts 2,2,1,1 because E appears twice, T appears twice, and L and R each appear once. Start from 6! and divide by 2! and 2! to remove duplicate swaps of the repeated letters.

Worked steps

Show your work

1. Inputs: item-group counts = 2, 2, 1, 1
2. Formula: T! / (n1! n2! n3! ...)
3. Substitute: 6! / (2! 2! 1! 1!)
4. Steps: start with 720 and divide by 2! = 2, 2! = 2, 1! = 1, 1! = 1
5. Result: For item-group counts 2, 2, 1, 1, the number of distinct arrangements is 180.