PermutationsFind permutations using permutation

notation and using technology.

Determines how many possible orders of objects

An arrangement of objects in a specific order◦ Order is important!

EX: In how many different orders can you watch 3 movies?

What is a Permutation?

When one event does NOT affect the outcome of another they are independent.

You can use the Multiplication Counting Principle to find the number of outcomes when events are independent.◦ If there are m ways to make a first selection and n ways

to make a second selection, then there are m ∙ n ways to make both selections.

EX:5 shirts and 8 shorts, how many possible outfits?◦ Shirts and shorts are independent of each other so there

are 5∙ 8 = 40 possible outfits

Independent Events

When events are dependent and occur without repeating you can use a permutation.

Ex: how many different batting orders can you have with 9 players?

You can have 9 ∙ 8 ∙ 7 ∙ 6 ∙ 5 ∙ 4 ∙ 3 ∙ 2 ∙ 1 = 362,880 possible orders

Or 9! which is read “9 factorial” n! is used to calculate a permutation.

◦ It is the product of all the integers from n to 1.◦ Keep in mind that the value of 0! is 1

Finding Permutations

nPr represents the number of permutations of n objects arranged r at a time.

Ex: arrange 8 objects into pairs with a first choice and a second choice.

8P2 =

You could also say that so 6! cancels and you have 8∙7=56

Permutation Notation

A band has 7 new songs and wants to put 5 of them on a demo CD. How many arrangements of 5 songs are possible?

7P5 =

You can use a graphing calculator as well.

Enter the number of objects then press MATH, left arrow, 2(nPr), enter the number chosen (r), ENTER

Practice

P.766 #12-26 All

Assignment