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# Counting Principle, Permutation & Combination - PowerPoint PPT Presentation

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

Dwayne Strachan

Edtech 597

Multiple Principle Lesson

Weeks 15-16

### 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

11

12

10

13

15

16

14

19

20

17

18

21

23

24

22

### 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

3 x 2 x 4

24

### 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.

3

5

4

x

x

= 60 different

dinners

### Permutation

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

• How many different permutations can I arrange them in?

A B C

A C B

B C A

B A C

C A B

C B A

6

x

5

x

4

x

3

x

2

x

1

720 arrangements

### The Permutation Notation

n = the number of items that can be used

r = the number of items that will be used

= 720 different

arrangements

0! = 1

### 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.

6

x

5

x

4

= 120 different

arrangements

A B C

A C B

B C A

B A C

C A B

C B A

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

n = the number of items that can be used

r = the number of items that will be used

### Combinations

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

• Go to the next page for the answer.

= 10 words

### 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.