A Permutation is an arrangement of items in a particular order.
Notice, ORDER MATTERS!
To find the number of Permutations of n items, we can use the Fundamental Counting Principle or factorial notation.
You can see that the number of permutations of 3 items is 3 · 2 · 1. You can extend this to permutations of n items, which is n · (n – 1) · (n – 2) · (n – 3) · ... · 1. This expression is called n factorial, and is written as n!.
A FACTORIAL is a counting method that uses consecutive whole numbers as factors.
The factorial symbol is !
Examples 5! = 5x4x3x2x1
7! = 7x6x5x4x3x2x1
Sometimes you may not want to order an entire set of items. Suppose that you want to select and order 3 people from a group of 7. One way to find possible
permutations is to use the Fundamental Counting Principle.
arrangements of 4 4!
Another way to find the possible permutations is to use factorials. You can divide the total number of arrangements by the number of arrangements that are not used. In the previous slide, there are 7 total people and 4 whose arrangements do not matter.