- Mistakes in Physics
- Natural Born Manipulators: 5 Ways To Drive You Crazy
- The Invention Handheld Clouds of Cotton Candy
- NASA X-planes
- Bionics: How People Imitate Nature
- An Aztec And A Box Of Chocolates
- Traces of the Ancient Seas
- Everyday Combinatorics
- The Lava Lamp
- The biggest wave on the Planet
- Fly Like a Bird
- Caves: Dungeons & Caverns
- Scientific Astrology
- How Has Coronavirus Changed The World ?
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 RULE OF SUM
The number of possible ways to select 1 object from 2 sets is equal to the total number of objects in these sets.
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.