bookstore, ordering of books A bookstore has 3 copies of the calculus book, 4 copies of the algebra book, and 5 copies of the statistics book.  How many different orders can they be arranged on a shelf?

My thinking:
12 books, so 12!
Let us start with a simpler example. Say we have the letters A,A,B. We need to find the total number of ways in which they can be arranged.

If we say "there are 3 letters so the total number should be $3!$", we are having repetitions such as AAB, AAB because we assumed that they were all distinct when they weren't. As you can see, a total of $2!$ arrangements are repeated among the $A$s alone, so we need to get rid of those by diving by $2!$, so we end up with $$\frac{3!}{2!}$$

Similarly, here we have 3 copies of one book, 4 copies of one, and 5 copies of one. We get rid of them by dividing for each of those, so we end up with $$\frac{12!}{3!\times 4!\times 5!}$$
Since the question mentions copies of the book, I will assume that copies are identical to each other. In this case, the number of ways is given by 
$$N = \frac{12!}{3!\times4!\times5!}$$