Snapshot 1: There is only one way to permute a list containing

elements into

(singleton) cycles, and therefore

.
Snapshot 2: Rotating the elements in a cycle so that the last becomes the first results in the same cycle:

is the same cycle as

. Because of this, it is often desirable to choose a standard representation of any cycle, such as rotating it so that its greatest element is listed first. After fixing the position of the greatest element in a list of

items, there are

ways to permute the remaining

elements to create different cycles, which means that

.