Permutations
Combinations are selections that disregard order. The powerset P(S) of a set S is the set of all possible combinations of the n elements of S. There are 2n of these. Permutations are arrangements of sequences into orders. The number of permutations of a set is denoted n! For example, the set {x, y, z} has 6 permutations : {x, y, z}, {x, z, y}, {y, x, z}, {y, z, x}, {z, y, x} and {z, x, y}. Suppose f exists that for given k provides all permutations of S that start with sk. All permutations could then be found by f with k ranging over [0, N - 1]. But f trivially exists as it can be computed by prepending sk to the permutations of the smaller set S - { sk }. Here are two programs to compute the permutations of a set based on this idea.
