## Counting methods

Hello,

So I have a question that I thought I did right but in reality, was wrong. The question goes as followed: Suppose I give you a list of 20 problems to study, from which I will randomly pick 14 questions for your first midterm exam.

For whatever reason, you prepare for the midterm exam by completing and understanding how to solve 12 questions of the 20, so there are 8 questions you do not know how to solve.
Part (a) What is the probability that you completely solve 5 of the 14 questions appearing on the midterm exam?

Part (b) To pass the midterm, you must correctly solve at least half of the 14 questions. What is the probability of you passing the midterm exam?

For Part A calculated that it should be (12C5)(8C9)/(20C14) but that is wrong. There is no way to chose 9 questions out of 8 thus making it 0, multiplying that by 12 chose 5 gives us 0 on the numerator thus making the probability 0, and I believe that it is highly unlikely for the probability to answer 5 questions out of 14 to be 0%.