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. See combinations.