Arrange the Word APPLE

Decision guide

Why this formula fits

This is a multiset permutation problem because the P appears twice, so duplicate swaps must be removed.

Does order matter? Order matters because changing letter positions creates a different arrangement.

Is repetition allowed? APPLE has item counts 2,1,1,1 because only P repeats, so the adjustment comes from dividing by 2!.

Worked solution

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

1. Inputs: item-group counts = 2, 1, 1, 1
2. Formula: T! / (n1! n2! n3! ...)
3. Substitute: 5! / (2! 1! 1! 1!)
4. Steps: start with 120 and divide by 2! = 2, 1! = 1, 1! = 1, 1! = 1
5. Result: For item-group counts 2, 1, 1, 1, the number of distinct arrangements is 60.