How many distinct arrangements of the letters in the country name CANADA are there?

Exact result

120

For item-group counts 3, 1, 1, 1, the number of distinct arrangements is 120.

CANADA has counts 3,1,1,1 because A appears 3 times while C, N, and D each appear once. Start from 6!, since we have six letters, and divide by 3! to remove duplicate swaps of the repeated As.

Worked steps

Show your work

1. Inputs: item-group counts = 3, 1, 1, 1
2. Formula: T! / (n1! n2! n3! ...)
3. Substitute: 6! / (3! 1! 1! 1!)
4. Steps: start with 720 and divide by 3! = 6, 1! = 1, 1! = 1, 1! = 1
5. Result: For item-group counts 3, 1, 1, 1, the number of distinct arrangements is 120.