The order of sets can be computer by summing the orders of subsets which every element of the set belongs to exactly one such subset.
Multplication Principle
Suppose we have a sequence of m decisions can be used to determine an element of a set S. Assume also that every element fo S is determined by exavtly one sequence of decisions. Finally, assume that the number of ways to make the ith decision is a number r_i, which does not depend on any of the preciously made decisions. then we have the order to the set can be computed by the product of ways to make each decision.