How many ways can the 10 A's be distributed? I'm stuck with the basic counting problem.
Problem is the following:

Corrupt professor Z has a class of 50 students. He needs to give exactly 10 A's. However five students already have a special deal (they are professor Z's nephews and neices) and will get A's for sure. How many ways can the 10 A's be distributed?

My thought : 45 Choose 5, because we can ignore 5 people(nephews and nieces) who will get A's grade for sure. 
I'm not sure my thought is correct or not. I'm appreciated any comment or explanation for this.

Yes it is 45 Choose 5 because you have 5 As and a population of 45 students to give it to.
