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

Exact result

420

For item-group counts 3, 2, 1, 1, the number of distinct arrangements is 420.

SUCCESS has counts 3,2,1,1 because S appears 3 times, C appears 2 times, and U and E each appear once. Start from 7! and divide by 3! and 2! to remove duplicate swaps of the repeated letters.

Worked steps

Show your work

1. Inputs: item-group counts = 3, 2, 1, 1
2. Formula: T! / (n1! n2! n3! ...)
3. Substitute: 7! / (3! 2! 1! 1!)
4. Steps: start with 5,040 and divide by 3! = 6, 2! = 2, 1! = 1, 1! = 1
5. Result: For item-group counts 3, 2, 1, 1, the number of distinct arrangements is 420.