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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

Counting Principle, Permutation & Combination

Dwayne Strachan

Edtech 597

Multiple Principle Lesson

Weeks 15-16

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
slide4

1

2

3

4

slide5

7

8

5

6

slide6

9

11

12

10

slide7

13

15

16

14

slide8

19

20

17

18

slide9

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 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.
slide20

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

slide22

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.