Problems III: Numbers and counting
1. Of the 182 students who are taking three first year core Mathematics modules (Reasoning, Algebra and Calculus), 129 like Reasoning, 129 like Algebra, 129 like Calculus, 85 like Reasoning and Algebra, 89 like Reasoning and Calculus, 86 like Algebra and Calculus, and 54 like all three modules. How many of the students like none of the core modules?
2. Of the 170 students who took all the first year core modules last year, 124 liked Reasoning, 124 liked Algebra, 124 liked Calculus, 10 liked only Reasoning, nobody liked only Algebra, 4 liked only Calculus and 2 liked none of the modules. How many students liked all three core modules?
3. At an international conference of 100 people, 75 speak English, 60 speak ...