One of my teachers gives his students essay finals. First, he tells us three numbers, A, B, and C. He gives us A essay questions to study before the test. He picks B essay questions to put on the test, and we must pick out C of them to answer. He tells us to study A-B+C of the given questions if we want to pass the final.

As a procrastinator, I only studied the night before. Luckily, some other students had taken the test a day early, and could tell me which of the questions the teacher had picked. Of course, the teacher would pick a different combination of questions to give to the rest of the students. After hearing which questions were given, I realized I needed to study N less questions than was necessary before!

Find N, generalizing to all possible A, B, and C.