Of the 180 students in a college course, $\dfrac{1}{4}$ of the students earned an A for the course, $\dfrac{1}{3}$ of the students earned a B for the course, and the rest of the students earned a C for the course. How many of the students earned a C for the course?

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A quarter of the students earned an A:

$$\frac{1}{4}\cdot 180 = 45$$

Students earning B:

$$\frac{1}{3}\cdot 180 = 60$$

Students with C:

$$180-45-60 = \boxed{75}$$