Of the 60 students in the drama club, 36 take mathematics, 27 take physics and 20 students take both mathematics and physics. How many drama club students take neither mathematics nor physics?
There are $36 - 20=16$ students taking only math, $27-20=7$ taking only physics, and 20 taking both.  That leaves $60-16-7-20=\boxed{ 17}$ students taking neither.