Thanks for your reply! We actually used that method in class, but I'd like to know how to do it this way as well.

I've made a little more progress, I think...

Let X be the set of all possible permutations.

That is, |X| = (26)^3 * (10)^3

Let A be the set of permutations containing at least one 0.

That is, 26^3 * 1*10^2

Let B be the set of permutations containing at least one O.

That is, 1*26^2 * 10^3

Would I now need to find the intersection of A and B and subtract that from X? How would I find that intersection?