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The module Combinatorics systematically counts things that can be enumerated. For example: how many different ice cream with three flavors there are, if you have ten different flavors to choose from. Or how many different four-digit PIN codes you can enter when you withdraw money, or how many handshakes there will be when ten people get together and everyone will shake hands with each other.
The part of mathematics that deals with this is called combinatorics, there are concepts such as variations, permutations and variations.
Combinatorics is strongly linked to probability. For example: what is the probability that you guess the right pin-code if you know that the numbers 2, 4, 6 and 7 are included and you have three chances? Then you have to figure out how many different PIN codes there which contain the numbers above by systematic counting. This kind of problems can be illustrated in this module with the help of tree diagrams. You can use different colors and letters as items for your studies.
Settings
In the menu at the top left are tabs where you can choose whether to demonstrate sequences or groups. In the Tables tab you will only get the table set-ups.
For sequences: You select the number of colors/letters and the length of the sequence. Here you can select, if you like, with or without repetition.
For groups: You choose the colors/letters and the group size. The diagram shows all the variations and the table all kinds of groups (combinations). If you click on a row in the table the corresponding variations in the table are shown within a gray box.
For tables: Just select the number of items.
Try out how it works by choosing few colors (or letters) and short sequences or small groups. With the tempo buttons, you can work in step or get the whole tree chart/table at once.
In the gray bar on the right are the expressions and results of the calculations with some explanation.
You can work a maximum of 16 colors (letters), but remember that the charts easily "swamp" of as there are so many variations, permutations or combinations.
If you click on the printer button, you can preview and copy the entire tree to the clipboard, send it to Word or print it.
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