Everyday Combinatorics

Everyday Combinatorics
Some claim that mathematics is merely an abstract science needed only in school. Arithmetic is seen as sufficient for everyday life — for counting money. What about the branch of mathematics known as combinatorics? It’s barely a part of the school curriculum, merely perceived as gymnastics for the mind, but it can be found everywhere — from the analysis of popular games, such as poker, to the creation of drugs.

The Two Rules of Combinatorics

Let’s start with the good news: in combinatorics, there are only two rules that you need to know. If you master these, then you will understand the whole of combinatorics, which will greatly simplify your life. How exactly? We will demonstrate this later on. The bad news is that understanding these rules is not that easy.


The number of possible ways to select 1 object from 2 sets is equal to the total number of objects in these sets.

Example of the rule of sum

Consider an example. If there are 6 girls and 4 boys in a class, then there are 6 + 4 = 10 ways to choose 1 student. What if we were talking about tables or chairs instead of boys and girls? It’s simple enough — the same operations would apply. But it is necessary to select a pair of objects, instead of just a single object: an object from each set (in this case, there are 2). In that case, the following rule can be applied.

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An astronaut floating in space above the earth, surrounded by particles and positrons.

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