Problem:
A school has 100 students and 5 teachers. In the first period, each student is taking one class, and each teacher is teaching one class. The enrollments in the classes are , and 5 . Let be the average value obtained if a teacher is picked at random and the number of students in their class is noted. Let be the average value obtained if a student is picked at random and the number of students in their class, including that student, is noted. What is ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The average class size when a teacher-that is, a class-is picked at random is given by
A randomly picked student has a chance of being in the class with 50 students, a chance of being in a class with 20 students, and a chance of being in a class with 5 students, so
The requested difference is .
The problems on this page are the property of the MAA's American Mathematics Competitions