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:
Case1: 4 letters are all different : 5C4 * 4!
Case2: 2 Letters are same, 2 Letters are different: 2C1 * 4C2 * 4!/2!
Case3: 2 letters are same, 2 letters are same: 2C1 * 1C1 * 4!/2!
Case4: 3 Same, 1 Different: 1C1 * 4 C 1 * 4!/3!
Add them all up at the end and you get the answer.
But did i do Case3 right?