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  2. Combination - Wikipedia

    en.wikipedia.org/wiki/Combination

    In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations).For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple and an orange; or a pear and an orange.

  3. Combinations and permutations - Wikipedia

    en.wikipedia.org/wiki/Combinations_and_permutations

    Combinations and permutations in the mathematical sense are described in several articles. Described together, in-depth: Twelvefold way; Explained separately in a more accessible way: Combination; Permutation; For meanings outside of mathematics, please see both words’ disambiguation pages: Combination (disambiguation) Permutation ...

  4. Twelvefold way - Wikipedia

    en.wikipedia.org/wiki/Twelvefold_way

    In combinatorics, the twelvefold way is a systematic classification of 12 related enumerative problems concerning two finite sets, which include the classical problems of counting permutations, combinations, multisets, and partitions either of a set or of a number.

  5. Replication (statistics) - Wikipedia

    en.wikipedia.org/wiki/Replication_(statistics)

    In engineering, science, and statistics, replication is the process of repeating a study or experiment under the same or similar conditions to support the original claim, which is crucial to confirm the accuracy of results as well as for identifying and correcting the flaws in the original experiment. [1]

  6. Enumerative combinatorics - Wikipedia

    en.wikipedia.org/wiki/Enumerative_combinatorics

    The problem of finding a closed formula is known as algebraic enumeration, and frequently involves deriving a recurrence relation or generating function and using this to arrive at the desired closed form. Often, a complicated closed formula yields little insight into the behavior of the counting function as the number of counted objects grows.

  7. Permutation - Wikipedia

    en.wikipedia.org/wiki/Permutation

    A k-combination of a set S is a k-element subset of S: the elements of a combination are not ordered. Ordering the k-combinations of S in all possible ways produces the k-permutations of S. The number of k-combinations of an n-set, C(n,k), is therefore related to the number of k-permutations of n by: (,) = (,) (,) = _! =!

  8. Linear combination - Wikipedia

    en.wikipedia.org/wiki/Linear_combination

    In mathematics, a linear combination or superposition is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of x and y would be any expression of the form ax + by, where a and b are constants).

  9. Inclusion–exclusion principle - Wikipedia

    en.wikipedia.org/wiki/Inclusion–exclusion...

    The principle can be viewed as an example of the sieve method extensively used in number theory and is sometimes referred to as the sieve formula. [ 4 ] As finite probabilities are computed as counts relative to the cardinality of the probability space , the formulas for the principle of inclusion–exclusion remain valid when the cardinalities ...