for a survey of 80 law students it was found that 20 took probate law...

Question

20 took probate law, 40 took criminal law, and 12 took probate law but not crimimal law. How many of the 80 students took exactly one of these classes?

Answer 1

12 took just probate but not criminal law, which is taking exactly one of the two classes

20 took probate law so 8 took probate law and also criminal law

40 took criminal law, which includes the 8 who took both courses, leaving 40-8 = 32 who took just criminal law

that's 32 + 12 who took just one course or 44 students out of 80.

Criminal law is required. So all 80 must have taken criminal law, so maybe we should calculate 80-8 = 72 as those who just took one course. Add 72 to 12 = 84, which is impossible. Probate is an elective, but at this point apparently this law school didn't make criminal law an elective. That gets us back to 44 as the students who only took one of the two courses