• When all items are distinct, the number of permutations is n!n!n!.

• Identical items create “duplicate” arrangements (e.g., swapping two L’s in “BALLOON” doesn’t change the word).

• We divide by ni!n_i!ni​! for each repeated item to correct for overcounting.

Visual Idea: Use a side-by-side image showing:

1. All permutations of "AA" (just one unique arrangement)

2. All permutations of "AB" (2 arrangements)