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Information about Combinations

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, s 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

Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. It is related to many other areas of mathematics, such as algebra, probability theory, ergodic theory and geometry, as well as to applied subjects such as computer science
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For other senses of this word, see permutation (disambiguation).
Permutation is the rearrangement of objects or symbols into distinguishable sequences. Each unique ordering is called a permutation.
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SET may stand for:
  • Sanlih Entertainment Television, a television channel in Taiwan
  • Secure electronic transaction, a protocol used for credit card processing,

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subset of a set B if A is "contained" inside B. Notice that A and B may coincide. The relationship of one set being a subset of another is called inclusion or containment.
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In mathematics, an n-set is a set containing exactly n elements, where n is a natural number. Thus, every finite set is an n-set for some specific natural number n.
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In mathematics, particularly in combinatorics, a binomial coefficient is a coefficient of any of the terms in the expansion of the binomial (x+y)n.
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partition of a set X is a division of X into non-overlapping "parts" or "blocks" or "cells" that cover all of X. More formally, these "cells" are both collectively exhaustive and mutually exclusive with respect to the set being
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In mathematics, a combinadic is an ordered integer partition, or composition. Combinadics provide a lexicographical index for combinations. Applications for combinadics include software testing, sampling, quality control, and the analysis of gambling games such as Canada's national
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Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. It is related to many other areas of mathematics, such as algebra, probability theory, ergodic theory and geometry, as well as to applied subjects such as computer science
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In mathematics, a multiset (or bag) is a generalization of a set. A member of a multiset can have more than one membership, while each member of a set has only one membership. The term "multiset" was coined by Nicolaas Govert de Bruijn in the 1970s.
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For other senses of this word, see permutation (disambiguation).
Permutation is the rearrangement of objects or symbols into distinguishable sequences. Each unique ordering is called a permutation.
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This is a list of topics on mathematical permutations.
  • Alternating group
  • Alternating permutation
  • Bijection
  • Circular shift
  • Combination
  • Cycle index
  • Cycle notation
  • Cyclic order
  • Cyclic permutation
  • Derangement
  • Even and odd permutations

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Probability is the likelihood that something is the case or will happen. Probability theory is used extensively in areas such as statistics, mathematics, science and philosophy to draw conclusions about the likelihood of potential events and the underlying mechanics of
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