If there were not any duplicated (or triplicated) letters then there would be 6! or 720 ways to rearrange the letters. 6! = 6x5x4x3x2x1. This is because the first letter could be any of the 6 in the word tattoo. The 2nd letter could be any of the 5 remaining letters The 3rd could be any of the 4 remaining. The 4th could be any of the 3 remaining The 5th could be any of the 2 remaining The 6th has no choice = 1

Therefore if all letters were different there would be 6x5x4x3x2x1 ways = 720