05 permutations
Post on 03-Jun-2018
229 Views
Preview:
TRANSCRIPT
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 1/23
Permutations
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 2/23
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?
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 3/23
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.
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 4/23
Permutations
Real World Example:Five students are finalists in the school
spelling bee. How many ways can they
finish first, second, and third?
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 5/23
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
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 6/23
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)
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 7/23
Permutations
Example 1: Permutations.Find the value for P(5,2).
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 8/23
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)
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 9/23
Permutations
Example 2: Standing in Line.In how many different ways can Carlos,
Sergio, Caleb, DeMoris, Eric, and Brayton
stand in line?
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 10/23
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)
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 11/23
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?
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 12/23
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
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 13/23
Permutations
Example 4: Arrange letters in a word.In how many different ways can you
arrange the letters in the word rainbow?
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 14/23
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)
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 15/23
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?
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 16/23
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
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 17/23
Permutations
Independent Practice: Find the value.
(1) P(6,4) = ?
(2) How many ways can 4 books bearranged on a bookshelf?
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 18/23
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
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 19/23
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.
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 20/23
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)
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 21/23
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
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 22/23
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
8/11/2019 05 Permutations
http://slidepdf.com/reader/full/05-permutations 23/23
Homework:
- Core 01→ p.___ #___, all- Core 02 → p.___ #___, all
- Core 03 → p.___ #___, all
Permutations
top related