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.