![]() ![]() With a permutation, the order of numbers matters. Permutations differ from combinations, which are selections of some members of a set regardless of order. A permutation is the number of ways a set can be arranged or the number of ways things can be arranged. Consider a linear array A of N objects, numbering the positions in the array from 1 to N.A permutation, designated as is the following map: That is, moves the object in position k of the linear array A into position (k) this is the active convention, the objects are moved as the pieces on a chessboard. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. The total number of permutations of n distinct objects, taken r at a time, is defined by the permutation formula: An alternative symbol for a permutation is the relatively straightforward P ( n, r ). : often major or fundamental change (as in character or condition) based primarily on rearrangement of existent elements. ![]() In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. Mathematical version of an order change Each of the six rows is a different permutation of three distinct balls ![]()
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