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Combinatorics

Combinatorics is a branch of mathematics that studies the different ways in which objects or numbers can be arranged. It is the basis of many areas of mathematics, especially descriptive statistics and probability.

Combinatorics is a branch of mathematics that examines the various ways in which objects or numbers can be arranged. It is the basis of many areas of mathematics, especially descriptive statistics and probability.

Typical combinatorial problems include the following:

- How many different ways are there to place six people in the compartment of an ICE train?

- In how many ways can six numbers be chosen from 45?

- In how many ways can eleven things be arranged in three compartments?

The term "combinatorics" goes back to Gottfried Wilhelm Leibniz (1646 to 1716), who dealt with permutations, among other things. The actual founders, however, are Blaise Pascal (1623 to 1662) and Pierre De Fermat (1601 to 1665), who laid the foundations of probability theory in their correspondence. In addition to the contribution of Jakob Bernoulli (1654 to 1705), that of Leonhard Euler (1707 to 1783), who considered combinatorial problems such as the Königsberg bridge problem by means of graphs, is also worth mentioning.

Combinatorial problems can be solved by going back to the so-called basic tasks of combinatorics (permutations, variations and combinations). Working with the urn model is also helpful.

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