# In a certain department, 45 students are enrolled in a chemistry class, 37 students are enrolled in biology, and 16 students are enrolled in both. Assuming every student is in at least one of the courses, how many students are enrolled in exactly one course?

Jan 29, 2015

Your question is a bit ambiguous, especially by the use of the word "and" just before 16. There are two possibilities:

(1) (unlikely)
45 chemistry + 37 biology + 16 both.
Then the answer is simply 45+37=82

(2) (I think that's the one you mean)
45 chemistry + 37 biology = 82 course-places of which 16 do both, so they take 2 course-places each.
This means that 16 chemistry students also do biology
But also that 16 biology students also do chemistry (=the same students).

So $45 - 16 = 29$ chemistry students do only chemistry
And $37 - 16 = 21$ biology student do only biology

Answer : $29 + 21 = 50$ students do only one course.

Remark that the total number of students is $66$:
$29$ only bio, $21$ only chem, $16$ both.
(Actually I would have expected that question: What is the total number of students?)