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 of them were painters;

50 of them were electricians ;

50 of them were plumbers;

15 of them had skills in all three areas;

all of them had skills in at least one of these areas.

If he hired everyone who were 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?

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