Discrete Mathematics
# Principle of Inclusion and Exclusion

28,000 people read *NanJing Morning News*,

23,000 people read *NanJing Evening News*, and

4,000 people read both.

How many people read neither?

Katie is teaching a class of thirty pupils, of which fourteen are girls. She knows that there are twenty-two pupils who are right-handed.

What is the minimum number of girls who are right-handed in this class?

How many positive integers less than or equal to 60 are divisible by 3, 4, or 5?

At a construction site, Jorge is in charge of hiring skilled workers for the project. Out of 80 candidates that he interviewed, he found that

- 45 were painters,
- 50 were electricians,
- 50 were plumbers,
- 15 had skills in all three areas, and
- all of them had skills in at least one of these areas.

If he hired everyone who was skilled in exactly 2 areas, how many candidates were hired?

For the integers from 1 to 1000, how many multiples of 9 are also multiples of 6?