# permutations

English - English
plural of permutation
permutations and combinations
Number of ways a subset of objects can be selected from a given set of objects. In a permutation, order is important; in a combination, it is not. Thus, there are six permutations of the letters A, B, C selected two at a time (AB, AC, BC, BA, CA, CB) yet only three combinations (AB, AC, BC). The number of permutations of r objects chosen from a set of n objects, expressed in factorial notation, is n! (n -r)! The number of combinations is n! [r!(n -r)!]. The (r + 1)st coefficient in the binomial expansion of (x + y)^n coincides with the combination of n objects chosen r at a time (see binomial theorem). Probability theory evolved from the study of gambling, including figuring out combinations of playing cards or permutations of win-place-show possibilities in a horse race, and such counting methods played an important role in its development in the 17th century
permutation
A transformation of a set's prime form, by applying one or more of certain operations, specifically, transposition, inversion, and retrograde
permutation
A one-to-one mapping from a finite set to itself

This permutation takes each element to the one following it, with the last mapped back to the first.

permutation
An ordering of a finite set of distinct elements

There are six permutations of three elements, e.g. {abc, acb, bac, bca, cab, cba}.

permutation
reciprocal change, different ordering of same items
permutation
{n} an exchange of one for another
Permutation
alternation
permutation
A a particular ordering of a set of objects For example, given the set {1, 2, 3}, there are six permutations: {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}
permutation
A group of elements from a set in which the order of the elements is important
permutation
A permutation of a set is an arrangement of the elements of the set in some order If the set has n things in it, there are n! different orderings of its elements For the first element in an ordering, there are n possible choices, for the second, there remain n-1 possible choices, for the third, there are n-2, etc , and for the nth element of the ordering, there is a single choice remaining By the fundamental rule of counting, the total number of sequences is thus n×(n-1)×(n-2)× ×1 Similarly, the number of orderings of length k one can form from n>=k things is n×(n-1)×(n-2)× ×(n-k+1) = n!/(n-k)! This is denoted nPk, the number of permutations of n things taken k at a time C f combinations
permutation
complete change in character or condition; "the permutations taking place in the physical world"- Henry Miller
permutation
A situation in which order matters In general, the number of permutations of n things taken m at a time is denoted asP(n,m) and is calculated by evaluating the expression [DMTA, p 275]
permutation
{i} combination, act of reordering elements within a given set (Mathematics)
permutation
A permutation is one of the ways in which a number of things can be ordered or arranged. Variation among humans is limited to the possible permutations of our genes. one of the different ways in which a number of things can be arranged (permutacion, from , from permutare )
permutation
Barter; exchange
permutation
A permutation can be thought of in two ways: in passive form, it is an arrangement of the elements of a set in order; in active form, it is a one-to-one and onto function from the set to itself (so that the passive form is the image of the "natural" order of the set) For example, the permutation whose passive form is (2,4,1,3) is, in active form the function which maps 1 to 2, 2 to 4, 3 to 1, 4 to 3 Permutations in active form are functions and can be composed This composition is the group operation in the symmetric group
permutation
A permutation of the set of numbers {1, 2, , n} is a reordering of these numbers
permutation
The arrangement of any determinate number of things, as units, objects, letters, etc
permutation
in all possible orders, one after the other; called also alternation
permutation
The number of ways of selecting objects from n distinguishable objects without replacement when order of selection is important nPr =n (n-1) (n-2) (n-r+1)
permutation
A permutation is a way to order a set of things For example, if your set is the letters in the word WHO, then one other ordering would be WOH Here are all the possible orderings of the letters in the word WHO: WHO WOH HWO HOW OWH OHW There are 6 different ways to order the letters in the word WHO To learn more about permutations, see the permutation notes
permutation
taking place in the physical world"- Henry Miller the act of changing the arrangement of a given number of elements
permutation
Any one of such possible arrangements
permutation
Combination, n
permutation
act of changing the lineal order of objects in a group
permutation
an event in which one thing is substituted for another; "the replacement of lost blood by a transfusion of donor blood"
permutation
act of changing the lineal order of objects in a group complete change in character or condition; "the permutations
permutation
the act of changing the arrangement of a given number of elements
permutation
a combination of the affirmative and the counter plan simultaneously If the permutation is successful then the counter plan is not competitive
permutation
The act of permuting; exchange of the thing for another; mutual transference; interchange
permutation
Given an ordered set of elements, a permutation is a reordering of that set where each element appears exactly once For example, "egam" is a permutation of "game", or "2431" is a permutation of "1234"
permutation
Cf
permutations

## Turkish pronunciation

pırmyuteyşınz

## Pronunciation

/ˌpərmyo͞oˈtāsʜənz/ /ˌpɜrmjuːˈteɪʃənz/

## Etymology

[ "p&r-myu-'tA-sh&n ] (noun.) 14th century. Middle English permutacioun exchange, transformation, from Middle French permutation, from Latin permutation-, permutatio, from permutare.

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