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Permutations

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Permutations

Objectives:(1) Students will be able to usepermutations to find all possible

arrangements involving a limitednumber of choices.

Essential Questions:

(1) What are permutations and how canwe find them?

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Permutations

What is a Permutation?- Have you ever been in an ice cream shop

and wondered about all the different

ways you could order three differentscoops of ice cream?

- A PERMUTATION  is an arrangement orlisting in which order IS important.

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Permutations

Real World Example:Five students are finalists in the school

spelling bee. How many ways can they

finish first, second, and third?

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Permutations

Real World Example:Five students are finalists in the school

spelling bee. How many ways can they

finish first, second, and third?

P(5,3) = 5 x 4 x 3 = 60 different ways

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Permutations

How Do I Find The Value of A Permutation?

- We calculate the value of a permutationin the following way:

P(5,3) = 5 x 4 x 3 = 60 different ways

Start with this number

Count down this many numbers

(1) (2) (3)

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Permutations

Example 1: Permutations.Find the value for P(5,2).

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Permutations

Example 1: Permutations.Find the value for P(5,2).

P(5,2) = 5 x 4 = 20

Start with this number

We are using this many numbers so we count down this many numbers

(1) (2)

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Permutations

Example 2: Standing in Line.In how many different ways can Carlos,

Sergio, Caleb, DeMoris, Eric, and Brayton

stand in line?

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Permutations

Example 2: Standing in Line.In how many different ways can Carlos,

Sergio, Caleb, DeMoris, Eric, and Brayton

stand in line?

P(6,6) = 6 x 5 x 4 x 3 x 2 x 1 = 720 different ways

There are 6 people to choose from

We are selecting this many people

(1) (2) (3) (4) (5) (6)

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Permutations

Example 3: Video Games.If I choose three video games to play at

Celebration Station out of ten, in how

many different orders can I play thosethree games?

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Permutations

Example 3: Video Games.If I choose three video games to play at

Celebration Station out of ten, in how

many different orders can I play thosethree games?

P(10,3) = 10 x 9 x 8 = 720 different orders

We are selecting 3 games to play

(1) (2) (3)

There are 10 games to choose from

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Permutations

Example 4: Arrange letters in a word.In how many different ways can you

arrange the letters in the word rainbow?

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Permutations

Example 4: Arrange letters in a word.In how many different ways can you arrange

the letters in the word rainbow?

P(7,7) = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways

We are selecting all 7 letters

(1) (2) (3)

There are 7 different letters to arrange

(4) (5) (6) (7)

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Permutations

Guided Practice: Find the value.

(1) P(8,3) = ?

(2) How many ways can the three membersof the debating team be arranged on thestage?

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Permutations

Guided Practice: Find the value.

(1) P(8,3) = 8 x 7 x 6 = 336

(2) How many ways can the three membersof the debating team be arranged on thestage?

P(3,3) = 3 x 2 x 1 = 6 ways

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Permutations

Independent Practice: Find the value.

(1) P(6,4) = ?

(2) How many ways can 4 books bearranged on a bookshelf?

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Permutations

Independent Practice: Find the value.

(1) P(6,4) = 6 x 5 x 4 x 3 = 360

(2) How many ways can 4 books bearranged on a bookshelf?

P(4,4) = 4 x 3 x 2 x 1 = 24 ways

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Permutations

Real World Example: Ice Cream.Coldstone Creamery has a total of 31 different

flavors. They are running a special where you

can get three scoops for the price of one.How many ways can you order threedifferent flavored scoops.

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Permutations

Real World Example: Ice Cream.Coldstone Creamery has a total of 31 different

flavors. They are running a special where you

can get three scoops for the price of one.How many ways can you order threedifferent flavored scoops.

P(31,3) = 31 x 30 x 29 = 26,970 different ways

Start with this number

Count down this many numbers

(1) (2) (3)

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Permutations

Summary:- Permutations involve arrangements or

listings where order is important.

- We use the following notation:

P(9,4) =* The symbol P(9,4) represents the number of permutations of

9 possible things to take, and we are taking 4 of them

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Permutations

Summary:- Permutations involve arrangements or

listings where order is important.

- We use the following notation:

P(9,4) = 9 x 8 x 7 x 6 =

Start with this number

Count down this many numbersPermutation

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Homework:

- Core 01→ p.___ #___, all- Core 02 → p.___ #___, all

- Core 03 → p.___ #___, all

Permutations