Counting principle permutation combination
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Counting Principle, Permutation & Combination. Dwayne Strachan Edtech 597 Multiple Principle Lesson Weeks 15-16. The wardrobe of a clown. How many different costumes can I make?. I have three clown shirts I have two clown pants I have four clown shoes. 1. 2. 3. 4. 7. 8. 5. 6. 9.

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Counting Principle, Permutation & Combination

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Counting principle permutation combination

Counting Principle, Permutation & Combination

Dwayne Strachan

Edtech 597

Multiple Principle Lesson

Weeks 15-16


The wardrobe of a clown

The wardrobe of a clown


How many different costumes can i make

How many different costumes can I make?

  • I have three clown shirts

  • I have two clown pants

  • I have four clown shoes


Counting principle permutation combination

1

2

3

4


Counting principle permutation combination

7

8

5

6


Counting principle permutation combination

9

11

12

10


Counting principle permutation combination

13

15

16

14


Counting principle permutation combination

19

20

17

18


Counting principle permutation combination

21

23

24

22


The counting principle notation

The Counting Principle notation

The number of outcomes of an event is the product of the number of outcomes in each stage of the event.

m = the number of outcomes in the first stage

n = the number of outcomes in the second stage


The counting principle

The Counting Principle

3 x 2 x 4

24


The counting principle1

The Counting Principle

  • Let’s say you were out for dinner and had a choice of three appetizers, five entrees and 4 desserts.

  • How many different dinners could you create.

  • Go to the next page for the solution.


Counting principle

Counting Principle

3

5

4

x

x

= 60 different

dinners


Permutation

Permutation

  • I have six pictures I want to hang on the wall

  • How many different permutations can I arrange them in?


Permutation1

Permutation

A B C

A C B

B C A

B A C

C A B

C B A


Permutation2

Permutation

6

x

5

x

4

x

3

x

2

x

1

720 arrangements


The permutation notation

The Permutation Notation

n = the number of items that can be used

r = the number of items that will be used


Permutation3

Permutation

= 720 different

arrangements

0! = 1


Permutation4

Permutation

  • What do you think you would do if all pictures were not included in the arrangement?

  • Find the number of three picture arrangements that can be made from the six original pictures.

  • Go to the next page for the solution.


Counting principle permutation combination

6

x

5

x

4

= 120 different

arrangements


Combination

Combination

A B C

A C B

B C A

B A C

C A B

C B A


Counting principle permutation combination

Combination

Sue

Pat

Ben

Gus

Sue & Ben

Sue & Gus

Sue & Pat

Pat & Ben

Pat & Gus

Pat & Sue

Ben & Sue

Ben & Pat

Ben & Gus

Gus & Sue

Gus & Pat

Gus & Ben


The combination notation

The Combination Notation

n = the number of items that can be used

r = the number of items that will be used


Combinations

Combinations

  • How many different three letter nonsense words can be made from the word MATH?

  • Go to the next page for the answer.


Combination1

Combination

= 10 words


Counting principle permutation and combination

Counting Principle, Permutation and Combination

  • The counting principle will find the number of outcomes in an event.

  • A permutation is a unique arrangement of elements selected from a group of elements.

  • A combination is a group of objects selected from a group of elements without consideration of order.


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