Applications

So, why does this all matter? There are, of course, applications of permutations, or they would not exist. Let's consider the following problem where calculating permutations is necessary:

Consider a machine shop that has 10 orders that require the use of its one lathe. Those orders will have to be scheduled in order to meet deadlines, have material available, and satisfy other constraints. The order in which the orders are completed is a permutation. People who do scheduling are really creating permutations.