A college freshman must take a science course, a humanities course, and a mathematics course. If she may select any of 4 science courses, any of 3 humanities courses, and any of 2 mathematics courses, how many ways can she arrange her program?

Answer 1

4*3*2 = 24 different ways to choose,
Not quite sure what you mean by "arrange" but if that involves the order of classes, then
3! ways to schedule her 3 choices, so
24*6 = 144 possible schedules