There are some five courses offered in a semester. The group of students who tak
ID: 3532160 • Letter: T
Question
There are some five courses 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?
Explanation / Answer
Let there be x students taking all 5 courses.
Since 80 students are registered in each course. The sum of the number of students of all the subjects without subtracting students with common subjects 80*5 = 400
But 40 take exactly 2 subjects. So we have counted them twice in 400 students. Since 2 sets share these students. And so we have counted them twice in 400.
Similarly 20 take exactly 3 subjects. So we have counted them twice in 400 students. Since 3 sets share these students. And so we have counted them thrice in 400.
Similarly 10 take exactly 4 subjects. So we have counted them twice in 400 students. Since 4 sets share these students. And so we have counted them four tiimes in 400.