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.