To find out how many students earned a C for the course, we can follow these steps:

1. Total number of students: 180
2. Students who earned an A:
   $\frac{1}{4}$ of 180 = $\frac{1}{4} \times 180 = 45$ students
3. Students who earned a B:
   $\frac{1}{3}$ of 180 = $\frac{1}{3} \times 180 = 60$ students
4. Students who earned a C:
   The remaining students = $180 - 45 - 60 = 75$ students

So, 75 students earned a C for the course.

The correct answer is 75.

Would you like any further details or have any questions?

Here are some related questions:

1. What fraction of students earned either an A or a B?
2. How many students would earn a B if the total number of students was 240?
3. What percentage of students earned a C in this course?
4. If 10 students are added to the total, all of whom earn a C, how many students would have earned a C then?
5. If 30 students decided to drop the course, how many would have earned a C then?

Tip: Always check if you have accounted for all students when working with fractions or percentages of a total.