T o illustrate, consider counting the number of ways one can arrange Peter, Paul, and Mary with the order important. Listing the possibilities:

So, it is easy to see that these are all of the possible outcomes and that the total number of such outcomes is 6. What happens however if we add Simone to the list?

Notice how the list quickly grows when just one more choice is added. This example illustrates how keeping track of the number of items in a set can quickly get impossible to manage unless we can use a more mathematical approach that allows you to count the number of possibilities without having to list them all.