I'm working on example 1.18 in Casella & Berger and I'm confused by the solution.
The problem states:
If n balls are placed at random into n cells, find the probability that exactly one cell remains empty.
In the solutions manual, it states that there are $n^n$ total ways to place $n$ balls into $n$ cells. This implies the sampling method is ordered with replacement. I agree that the $n$ cells are sampled with replacement. But, why is it considered ordered?
My logic:
Let's pretend there are 3 cells. If I place a ball into {1,1,2}, {1,2,1}, or {2,1,1}, in the end I have 2 balls in cell 1, and 1 ball in cell 2. The ordering does not matter.
What am I misunderstanding here?