On a certain examination the student must answer 8 out of 12 questions including exactly 5 of the first six. In how many ways may he write the examination.?

Answer 1

well, there are 6 ways to answer 5 of the 1st 6 correctly (the same as the number of ways to get one of them wrong)

That leaves 6 questions, of which 4 can be chosen in 6C4 = 15 ways.

Each set of 4 can be answered in 2^4 ways.