Part: Cycles, Permutations, Combinations and Variations

The most common combinatorial operations are cycles, permutations, combinations and variations. Loosely speaking, and before we define these three operations more rigidly, cycles are circular arrangements of objects, in which there is no specific "first" or "last" object, but the order of the objects inside the cycle is important. Cycles are essentially the same as permutations with the difference, that the latter are arrangements of objects with distinguished first and last elements. 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 Cycles

Examples of Permutations

Examples of Combinations

Examples of Variations

  1. Definition: Cycles
  2. Definition: Permutations
  3. Theorem: Approximation of Factorials Using the Stirling Formula
  4. Definition: Combinations
  5. Proposition: Factorial

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