In a group of 100 students, 50 are taking a math class, 35 are taking an English class, and 38 are taking a Physics class. 20 are taking both the Math and English class, 15 are taking both the Math and Physics class, and 18 are taking both the English and Physics class, and 8 are taking all three classes. (a) How many are taking at least one of of these three classes?
(b) How many are not taking any of these classes?