How Many Ways to distribute six different books among 13 children if no child gets more than one book?

So I think the issue right now is I may have thought too deeply about the question. 

Initially I thought the solution was C(13,6), but then I began to wonder what exactly the question is asking. Are there 6 different types of books and each child will get one? which would mean a solution like $6^{13}$. 

Then I also thought, "what about the children who don't get books, do I have to account for all the different ways that can occur too? So that would be something of the sort $C(13,6) X 7!$ 

I know I am overthinking, but how far am I going?