How many 3 letter words possible with the word Abacus? I am having difficulty solving this. I know that 6 letter words possible with abacus is (6! / 2! ). But my doubt is what happens when we have to choose 3 letters from abacus and how will we handle the repeating of the double a.

Hint:

1. How many three-letter words can you make with no $a$'s?
2. How many with exactly one $a$?
3. How many with both $a$'s?



These are disjoint sets so you can add them up.