Problem:
How many ways can a student schedule 3 mathematics courses algebra, geometry, and number theory - in a 6-period day if no two mathematics courses can be taken in consecutive periods? (What courses the student takes during the other 3 periods is of no concern here.)
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are choices for the periods in which the mathematics courses can be taken: periods ; periods ; periods and periods . Each choice of periods allows ways to order the 3 mathematics courses. Therefore there are ways of arranging a schedule.
The problems on this page are the property of the MAA's American Mathematics Competitions