permutations counting!. what is a permutation? permutations essentially answer the question “how...

PermutationsCOUNTING!

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!

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

Example How many ways can I rearrange the five books?

Is there an easier way?

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

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?

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

Let’s Check with our Last Question

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

Correct Notation

Example Evaluate:

₄P₂

₇P₃

₆P₅

Example

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

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

Example Cont.

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

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

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

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

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