2.2 Permutations (Textbook Section 4.6)

Recall Factorial Notation  The number of ways to arrange n objects into n spots is n! (read “!” a “factorial”)  It is calculated as follows n! = n x (n-1) x (n-2) x … x 3 x 2 x 1  i.e. 4! = 4 x 3 x 2 x 1

What if you have fewer than n spots?  Yesterday, we used factorial notation to arrange n objects into n spots  Today, we will look at how to arrange n objects into a r spots

Permutations  A permutation is an ordered selection of elements taken from a given set  Note: “ordered” means that the position of the element matters (i.e. labeling, arranging, assigning position, etc.)  Symbolically, it is the number of ways to arrange n objects into r spots

Notation  The notation for a permutation is n P r or P(n,r)  Think of the “P” as “pick”  i.e. “Given n objects, how many ways can you pick and arrange them into r spots ?”

Formula  Permutations are calculated using the following formula n P r = n!/(n-r)!  i.e. 5 P 2 = 5!/(5-2)! = 5!/3! = 20