Definition

A PERMUTATION of objects is an arrangement of those objects in some order. Some object is placed in the first position, another in the second position, and so on, until all objects have been placed.
For our purposes, a permutation is a string a(1), a(2), ..., a(n), where each a(i) is an element of the set [n] = {1,2,...,n} and each element occurs precisely once.
For example, the permutations of [3] = {1,2,3} are 123, 132, 213, 231, 312, 321. These permutations correspond to the six permutations given in the introduction, with 1 = Bob, 2 = Sally, and 3 = Pete.
In a K-PERMUTATION, only the first k positions have objects placed in them. For this example, only Bob and Pete may have arrived at the movies, but they are saving Sally's position in line. In this case, only the first 2 (k) positions have people (objects) in them.