Principle of Inclusion - Exclusion There are 213 students in the school. 89 students take humanities, 85 students take geometry, 83 students take computer science, and 77 students take chemistry. 28 students take both humanities and chemistry, 46 students take both humanities and geometry, 40 students take both geometry and computer science, and 30 students take both chemistry and computer science.15 students take humanities, chemistry and geometry, 16 students take humanities, geometry and computer science,
8 students take geometry, computer science and chemistry, and 12 students take computer science, chemistry and humanities. There are no students who take only humanities and computer science, and no students who take only geometry and chemistry. There are only 5 students who take all 4 classes. How many students take none of the classes?