Problem:
A student must choose a program of four courses from a menu of courses consisting of English, Algebra, Geometry, History, Art, and Latin. This program must contain English and at least one mathematics course. In how many ways can this program be chosen?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because English is required, the student must choose of the remaining courses. If the student takes both math courses, there are possible choices for the final course. If the student chooses only one of the possible math courses, then the student must omit one of the remaining courses, for a total of programs. Hence there are programs.
Because English is required, there are remaining courses from which a student must choose . Of those possibilities, one does not include a math course. Thus the number of possible programs is .
The problems on this page are the property of the MAA's American Mathematics Competitions