I am having trouble understanding how to solve this question:
Some five courses are offered in a semester. The group of students who take at least one of these courses consists of 155 students. There are 80 students registered in each course. For any two among these courses, there are precisely 40 students who take each of them. For any three of these courses, there are precisely 20 students who take each of them. For any four among these courses, there are precisely 10 students who take each of them. How many students in this group take every one among the five courses in this semester?
What I came up with is using a diagram I created to try and figure the problem out.
Course 1: has 40 people unaccounted for.
Course 2: has 30 people unaccounted for.
Courses 3 & 4 & 5: has 50 people unaccounted for.
By this process, only 30 people can take all five classes, but that leaves out 10 people in course 1 and 20 people in courses 3, 4 and 5.
This question comes from some inclusion/exclusion notes from my professor. The notes don't really explain inclusion/exclusion very well, or at least I don't understand it.
What am I missing? Can someone help me understand how to solve this question?