k-Combinations Without Replacement

A k-Combinations Without Replacement is a combination function that reports the number of k-Combinations within a Set composed of Distinct Set Members.

• AKA: C, ChoseNoR, Chose Function.
• Context:
  • domain: Set S and Non-Negative Integer k.
  • range: Non-Negative Integer.
  • It can be calculated as: n! / (k!(n-k)!), where n is the Set Cardinality(S).
• See: k-Combinations With Replacement, Card Draw Experiment.

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References

2009

• (Wikipedia, 2009) http://en.wikipedia.org/wiki/Combinations
  • In combinatorial mathematics, a combination is an un-ordered collection of distinct elements, usually of a prescribed size and taken from a given set. (An ordered collection of distinct elements would sometimes be called a permutation, but that term is ambiguous.) Given such a set S, a combination of elements of S is just a subset of S, where as always for (sub)sets the order of the elements is not taken into account (two lists with the same elements in different orders are considered to be the same combination). Also, as always for (sub)sets, no elements can be repeated more than once in a combination; this is often referred to as a "collection without repetition". For instance, {1,1,2} is not a combination of three digits; as a set this is the same as {1,2,1} or as {2,1,1}. On the contrary, a poker hand can be described as a combination of 5 cards from a 52-card deck: the order of the cards doesn't matter, and there can be no identical cards among the 5.
  • A k-combination (or k-subset) is a subset with k elements.

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