Hello, Saibot!

This is my solution to the following question. Case 3, seems to be wrong though.

How many 4-letter arrangements of the word TOMORROW are there?

So i separate letters into their own "buckets": T, OOO, M, RR, W

So here are the cases:

Case 1: 4 letters are all different: .

Case 2: 2 Letters are same, 2 Letters are different: .

Case 3: 2 letters are same, 2 letters are same: .

Case 4: 3 Same, 1 Different: .

Add them all up at the end and you get the answer.

But did i do Case 3 right?

Case 3: Two letters are same, two letters are same.

The four letters must be:

And there are: . arrangements.