Problem 17 - Precalculus with Limits

Question

A college student is preparing a course schedule for the next semester. The student may select one of two mathematics courses, one of three science courses, and one of five courses from the social sciences and humanities. How many schedules are possible?

Step-by-Step Solution

Answer

The total number of possible schedules is 30.

Step 1: Total Mathematics Courses Selection

The student can select one of two mathematics courses, hence there are 2 ways to do this.

Step 2: Total Science Courses Selection

The student can select one of three science courses, hence there are 3 ways to do this.

Step 3: Total Social Sciences and Humanities Courses Selection

The student can select one of five courses from social sciences and humanities, hence there are 5 ways to do this.

Step 4: Total Possible Schedules

By the multiplication principle, the total number of possible schedules (combinations of selections) is the product of the number of ways to make each selection. So the total number of possible schedules is \(2 (from Step 1) \times 3 (from Step 2) \times 5 (from Step 3) = 30\)