Counting the Number of Elements in an Intersection A professor in a discrete mathematics class passes out a form asking students to check all the mathematics and computer science courses they have recently taken. The finding is that out of a total of 50 students in the class, 30 took precalculus; 18 took calculus; 16 took both precalculus and Java; 8 took both calculus and Java; 47 took at least one of the three courses. 26 took Java; 9 took both precalculus and calculus; (a) How many students took all the three courses? (b) How many students took precalculus and calculus but not Java? 2/8

This is a solution for the question but I am not able to understand how to find an intersection (  it says n(P ∩ C ∩ J) = 6. ) I didn't understand how we get 6. Please check the images for the question.

a). Let P denote the set of students who took precalculus, C those who took
calculus, and J those who took Java.
(a) The answer is n(P ∩ C ∩ J). So let us write the inclusion-exclusion principle with
three subsets and replace the known terms with the given data:
n(P ∪ C ∪ J) = n(P) + n(C) + n(J) − n(P ∩ C) − n(P ∩ J) − n(C ∩ J) + n(P ∩ C ∩ J)
47 = 30 + 18 + 26 − 9 − 16 − 8 + n(P ∩ C ∩ J)
It follows that n(P ∩ C ∩ J) = 6.