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# Principle of Inclusion and Exclusion

Count to 100. How many of those numbers are odd or multiples of 5? Since 50 are odd and 20 are multiples of 5, at first glance the answer is 70...

Winston must choose 4 classes for his final semester of school. He must take at least 1 science class and at least 1 arts class. If his school offers 4 (distinct) science classes, 3 (distinct) arts classes and 3 other (distinct) classes, how many different choices for classes does he have?

**Details and assumptions**

He cannot take the same class twice.

Senior students at Brilliant High School are required to take at least one class in Geometry, Combinatorics, or Number Theory. They may take a class in more than one subject. If \(88\) student are taking Geometry, \(98\) students are taking Combinatorics, \(96\) students are taking Number Theory, \(11\) students are taking Geometry and Combinatorics, \(24\) students are taking Geometry and Number Theory, \(19\) students are taking Combinatorics and Number Theory, and \(6\) students are taking all the classes, how many students are in the senior class at Brilliant High?

**Details and assumptions**

When we say that \(88\) students are taking Geometry, these students may be taking Combinatorics and/or Number Theory as well.

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