Transcript Permutations.

Permutations
Permutations
Objectives:
(1) Students will be able
permutations to find all
arrangements
involving
a
number of choices.
to use
possible
limited
Essential Questions:
(1) What are permutations and how can
we find them?
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 different
scoops of ice cream?
- A PERMUTATION is an arrangement or
listing in which order IS important.
Permutations
Real World Example:
Five students are finalists in the school
spelling bee. How many ways can they
finish first, second, and third?
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
Permutations
How Do I Find The Value of A Permutation?
- We calculate the value of a permutation
in the following way:
Start with this number
P(5,3) = 5 x 4 x 3 = 60
(1)
(2)
Count down this many numbers
(3)
different ways
Permutations
Example 1: Permutations.
Find the value for P(5,2).
Permutations
Example 1: Permutations.
Find the value for P(5,2).
Start with this number
P(5,2) = 5 x 4 = 20
(1)
(2)
We are using this many numbers so we count down this many numbers
Permutations
Example 2: Standing in Line.
In how many different ways can Carlos,
Sergio, Caleb, DeMoris, Eric, and Brayton
stand in line?
Permutations
Example 2: Standing in Line.
In how many different ways can Carlos,
Sergio, Caleb, DeMoris, Eric, and Brayton
stand in line?
There are 6 people to choose from
P(6,6) = 6 x 5
(1)
(2)
x
4 x 3 x 2 x 1 = 720
(3)
(4) (5)
We are selecting this many people
(6)
different ways
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 those
three games?
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 those
three games?
There are 10 games to choose from
P(10,3) = 10 x 9 x 8 = 720
(1)
(2)
(3)
We are selecting 3 games to play
different orders
Permutations
Example 4: Arrange letters in a word.
In how many different ways can you
arrange the letters in the word rainbow?
Permutations
Example 4: Arrange letters in a word.
In how many different ways can you arrange
the letters in the word rainbow?
There are 7 different letters to arrange
P(7,7) = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040 ways
(1)
(2)
(3)
We are selecting all 7 letters
(4)
(5)
(6)
(7)
Permutations
Guided Practice: Find the value.
(1) P(8,3) = ?
(2) How many ways can the three members
of the debating team be arranged on the
stage?
Permutations
Guided Practice: Find the value.
(1) P(8,3) = 8 x 7 x 6 = 336
(2) How many ways can the three members
of the debating team be arranged on the
stage?
P(3,3) = 3 x 2 x 1 = 6 ways
Permutations
Independent Practice: Find the value.
(1) P(6,4) = ?
(2) How many ways can 4 books be
arranged on a bookshelf?
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 be
arranged on a bookshelf?
P(4,4) = 4 x 3 x 2 x 1 = 24 ways
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 three
different flavored scoops.
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 three
different flavored scoops.
Start with this number
P(31,3) = 31 x 30 x 29 = 26,970
(1)
(2)
Count down this many numbers
(3)
different ways
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
Permutations
Summary:
- Permutations involve arrangements or
listings where order is important.
- We use the following notation:
Start with this number
P(9,4) = 9 x 8 x 7 x 6 =
Permutation
Count down this many numbers
Permutations
Homework:
- Core 01 → p.___ #___, all
- Core 02 → p.___ #___, all
- Core 03 → p.___ #___, all