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Page 1: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

PermutationsCOUNTING!

Page 2: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

What is a Permutation? Permutations essentially answer the question “How many ways?”

When we talk about permutations, the ORDER in which things happen matters

For example, Alice, Bob, and Charlie is different than Charlie, Bob, and Alice

ORDER MATTERS!

Page 3: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Permutations Permutations are different than Combinations in the sense that order does not matter when we are calculating combinations

In the case of a combination, Alice, Bob, and Charlie is the same as Charlie, Bob and Alice.

It is the same COMBINATION of names

Page 4: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER
Page 5: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER
Page 6: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Example How many ways can I rearrange the five books?

Page 7: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Is there an easier way?

Page 8: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER
Page 9: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER
Page 10: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Try Another Example How many ways can you rearrange 8 different books?

Page 11: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Question What if we have 8 books but there are only three places on the shelf? How many ways can we rearrange the three books on the shelf?

Page 12: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Try It You have 10 books and want to arrange 4 on a shelf. How many ways can you do it?

Page 13: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER
Page 14: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Let’s Check with our Last Question

Page 15: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

How many ways can you arrange your 10 books on a four book shelf?

Page 16: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Correct Notation

Page 17: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Example Evaluate:

₄P₂

₇P₃

₆P₅

Page 18: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Example

Page 19: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Example How many ways can you rearrange the letters in GUITAR?

Page 20: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Example How many ways can you rearrange the letters in booger?

Page 21: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Example Cont.

Page 22: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Example How many ways can we rearrange the letters in Mississippi?

Page 23: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Example 10 Students are running for student council. How many ways can they be selected as President, Secretary, and Treasurer?

Page 24: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Example How many different six-digit numerals can be written using all of the following six digits: 4,4,5,5,5,7

Page 25: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Example In how many different ways can Travis, Noah, Kyle, Heather, Michael, Jacob, and Cody stand in line?

Page 26: Permutations COUNTING!. What is a Permutation? Permutations essentially answer the question “How many ways?” When we talk about permutations, the ORDER

Example Six coins are tossed at a time. How many outcomes show 4 heads and 2 tails?


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