Here's the problem:

There are 12 books on a shelf. If four of them are blue, how many combinations have all four books together? (then it asks to explain)

Here's what I did:

Ok, so there's 12 books, that's 12!. But then, there are two sets: one for blue books and one for the others. So the set for the blue books is 4! and the other is (12-4)! or 8!. So I ended up with this:

Is this right? I have no way of checking. Also any tips on ways to think of and attack these problems would be nice.

Thanks!