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In Combinatorial Mathematics , a combination is an un-ordered collection of unique elements. (An ordered collection is called a Permutation .) Given ''S'', the Set of all possible unique elements, a combination is a Subset of the elements of ''S''. The order of the elements in a combination is not important (two lists with the same elements in different orders are considered to be the same combination). Also, the elements cannot be repeated in a combination (every element appears uniquely once); this is often referred to as "without replacement/repetition". This is because combinations are defined by the elements contained in them, so the set {1, 1, 1} is the same as {1}. For example, from a 52-card deck any 5 cards can form a valid combination (a Hand ). The order of the cards doesn't matter and there can be no repetition of cards. A ''k''-combination (or ''k''-subset ) is a subset with ''k'' elements. The number of ''k''-combinations (each of size ''k'') from a set ''S'' with ''n'' elements (size ''n'') is the Binomial Coefficient : As an example, the number of five-card hands possible from a standard fifty-two card deck is: : A combination is a special case of a Partition Of A Set ; specifically, a partition into two sets of size ''k'' and ''n'' − ''k''. Since it is impractical to calculate if the value of ''n'' is very large, a more efficient algorithm is : Example: : SEE ALSO EXTERNAL LINKS
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