Distribution of different objects into different boxes We want to put n different objects into n different boxes. In how many ways can we do this if we want that exactly two boxes remain empty?

I have this problem for homework at the moment. Here is my try: That number corresponds to ${n \choose 2} $ times the number of surjective functions from $\{1,2,\dots n\}$ to $\{1,2,\dots, n-2\}$. Namely, we first choose boxes that will be empty and for other boxes $n-2$ of them we know that they will have "preimage" in the set of objects.
