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Discrete Mathematics

Principle of Inclusion and Exclusion

Principle of Inclusion and Exclusion Problem Solving

         

After a grueling nationwide examination, it was announced that
70% of students passed the Mathematics examination, and
60% of students passes the Science examination.

What is the minimum percentage of students that passed both examinations?

In a class of students, \(64\text{%}\) of the students passed the physics exam and \(68\text{%}\) of the students passed the math exam. What is the minimum percentage of students in the class that passed both exams?

How many numbers in the set \(\{1,2,\ldots,100\}\) are divisible by \(5\) or \(7?\)

A party of \(370\) vile creatures is marching through the woods. Each of the creatures is either an orc, a goblin, or a half-orc/half-goblin. If there are \(206\) creatures that are at least partly goblin, and \(211\) creatures that are at least partly orcs, how many of the creatures are half-orc/half-goblins?

Consider all \(4\)-digit positive numbers using all of the digits \(\{1, 2, 3, 4\}\). How many of these numbers have even first or second digit?

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