In the senior year of a high school graduating class of 600 students, 180 studied math, 200 studied chemistry, 240 studied history, 85 studied history but neither chemistry nor math, 75 studied both math and history, 35 studied chemistry but neither math nor history, 50 studied all three subjects. If a student is selected at random, find the probability.
(a) that a person takes all three subjects given that he or she enrolled in chemistry
(b) that a person takes both history and chemistry given that he or she is not taking math
(c) that a person did not take any of the three subjects