Permutations differ from combinations, which are selections of some members of a set regardless of order. The word "permutation" also refers to the act or process of changing the linear order of an ordered set. The group of all permutations of a set M is the symmetric group of M, often written as Sym ( M ). 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. In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations in G (which are thought of as bijective functions from the set M to itself). Not an initial condition, but related: c(n, k) 0 for k > n since the permutation of n with the most cycles is (1)(2) (n). Mathematical version of an order change Each of the six rows is a different permutation of three distinct balls since every permutation of n must have at least one cycle.
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