I got stuck on a simple problem which is part of a bigger problem.
So OK... All strings of length n from the letters A,B,C are $3^n$.
But how many of them contain at least one A and at least one B and at least one C ?!
I am getting $3^{n} - 3 \cdot 2^{n} + 3$ when I apply the inclusion-exclusion principle.
But I am not sure in this answer.