# 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.

## 1 Answer

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

• Let me check a minor issue in this problem. since the grade A's are not distinguishable, so that it cause 45 Choose 5. Is this also correct? – D.Choi Aug 31 '16 at 0:36
• Yes. Because the A's are not distinguishable it makes it a "Choose" – Q the Platypus Aug 31 '16 at 0:38
• Specifically: What you are choosing are five from forty-five distinct students to receive the A-marks. The A-marks not being distinguishable (nor the 40 other marks) means you don't have to count arrangements among themselves. – Graham Kemp Aug 31 '16 at 1:01