A class has 30 students, 17 have taken science, 19 have taken arts and two students have enrolled in any course. How many students enrolled in both science and Arts?

Let x = number of students enrolled in both Science and Arts.

Then the number of students taking Science only is 17 - x and,

the number of students taking Arts only is 19 - x.

We know that

Total # of students in class = # Science only + # Arts only + Both Arts & Sciences + # Any

= (17 - x) + (19 - x) + x + 2

= 38 + x

This should be equal to 30 as given. So,

38 - x = 30

Subtract 38 from both sides:

-x = - 8

So x = 8.

Answer: 8