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Permutations, Combinations and Variations

The most common combinatorial operations are permutations, combinations and variations. Loosely speaking, and before we define these three operations more rigidly, permutations are (finite or infinite) arrangements of objects. Here, the order of the objects is important. Combinations are the different ways to pick a finite number of objects out of another finite number of objects. Unlike for permutations, in combinations, the order of objects picked usually does not play any role. A combination, in which order does play a role, is called a variation.

Examples of Permutations

Examples of Combinations

Examples of Variations

| | | | created: 2019-09-10 19:41:47 | modified: 2019-09-10 20:01:49 | by: bookofproofs

1.Definition: Permutations

2.Theorem: Approximation of Factorials Using the Stirling Formula

3.Proposition: Factorial

4.Definition: Combinations

Edit or AddNotationAxiomatic Method

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Bibliography (further reading)