TOPIC: Probability Theory
Combinatorics
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What is this module about?

The term "Combinatorics" includes various rules serving to compute the number of combinations of elements which belong to a special set. In the following, these rules will be illustrated. They enable everyone to compute probabilities subject to the model of the same probabilities.



  EXAMPLE
Combinatorics: examples of use

  • In order to encode a text, one way is to producea so-called "random alphabet" by dicing. For that purpose, the alphabet has to be written in a row and the "random" alphabet in a second row below. The original text is now substituted according to the relationship between the two alphabets. The encoder"s task is then to detect the right allocation. If we regard the number of random alphabets the difficulty of this subject will be obvious.

  • How many ways exist to choose 6 numbers from 49 (lotto)?

  • How many ways exist to form an order of persons which participate in an examination?

EXERCISES
Permutations
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13
EXAMPLES
Combinatorics: examples of use
Permutations
Examples for samples without replication but regarding the order
Samples with replication with regarding the order
Samples without replication and disregarding the order
Samples with replication but disregarding the order
MATERIAL
Weblinks
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www.lernmoduleditor.de