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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

- I have three clown shirts
- I have two clown pants
- I have four clown shoes

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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

- 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

- 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

n = the number of items that can be used

r = the number of items that will be used

= 720 different

arrangements

0! = 1

- 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

n = the number of items that can be used

r = the number of items that will be used

- How many different three letter nonsense words can be made from the word MATH?
- Go to the next page for the answer.

= 10 words

- 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.