Question 61
In a school with $n$ students, a team of students must be chosen to clean the school. A team of students is called *good* if the school principal believes that they can manage to clean the school. It is known that at least one team is good, and that if a team is good, then it is also good after adding any other student. Show that the average number of students in good teams is at least $\frac{n}{2}$.