Final answer:
Using the principle of inclusion-exclusion, adding the number of students who've taken calculus and discrete mathematics, and then subtracting the number who've taken both, 427 students have taken at least one of those courses.
Step-by-step explanation:
To calculate the number of students at this college who have taken a course in either calculus or discrete mathematics, we use the principle of inclusion-exclusion. This principle provides a way to count the total number of elements in a union of two sets by adding the number of elements in each set and then subtracting the number of elements that are in both sets.
The number of students who have taken calculus is 375, and the number of students who have taken discrete mathematics is 212. However, there are 160 students who have taken both. Therefore, we need to adjust our total to avoid double-counting those students. Using the formula:
Total = Calculus + Discrete Mathematics - Both
We get:
Total = 375 + 212 - 160
After calculating, we find that:
Total = 427
Therefore, 427 students have taken either a calculus course or a discrete mathematics course.