Let’s count – Counting intersections

Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the complete solution of the exercises in the video or in the pdf below.

Exercise 1.

Suppose that in a bookstore there are 200 books, 70 in French and 100 dealing with a mathematical topic. How many books are there not written in French and not dealing with Mathematics if there are 30 books in French dealing with Mathematics?

Exercise 2.

A group of 200 students are eligible to take three Mathematics courses: Discrete Mathematics, Analysis, and Geometry. Each course has 80 students. Each pair of courses has 30 students in common, and 15 students are taking all three courses. 1. How many students are not taking any of the three mathematics courses? 2. How many students are taking only Discrete Mathematics?

Exercise 3.

How many 10-sequences of (I_9) are there in which the digits 1, 2, and 3 all appear?