3. Should the mathematics department in Exercise 2 revise the assignments for its TAs? Grades have been posted for the previous semester, and some students need to repeat the previous level of the course. A total of 45 students move from Calculus II to Calculus I, 41 students move from Calculus III to Calculus II, and 12 students move from Calculus IV to Calculus III.
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No, although if the quotas are rounded in the usual way, there will be 21 sections. One must reduce the apportionment of one course, and a logical way to do so will lead to the original apportionment.