10-8 Permutations Vocabulary permutation factorial.

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10-8 Permutations Vocabulary permutation factorial

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10-8 Permutations In how many ways can you arrange the letters A, B, and T ? Additional Example 1: Using a List to Find Permutations Use a list to find the possible permutations. There are 6 ways to order the letters. T, B, AB, T, AA, T, B T, A, BB, A, TA, B, T

Transcript of 10-8 Permutations Vocabulary permutation factorial.

Page 1: 10-8 Permutations Vocabulary permutation factorial.

10-8 Permutations

Vocabularypermutationfactorial

Page 2: 10-8 Permutations Vocabulary permutation factorial.

10-8 Permutations

An arrangement of objects or events in which the order is important is called a permutation.You can use a list to find the number of permutations of a group of objects.

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10-8 Permutations

In how many ways can you arrange the letters A, B, and T ?

Additional Example 1: Using a List to Find Permutations

Use a list to find the possible permutations.

There are 6 ways to order the letters.

T, B, AB, T, AA, T, BT, A, BB, A, TA, B, T

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10-8 PermutationsCheck It Out: Example 1

In how many ways can you arrange the colors red, orange, blue?

Use a list to find the possible permutations.

There are 6 ways to order the colors.

red, orange, bluered, blue, orangeorange, red, blueorange, blue, redblue, orange, redblue, red, orange

List all permutations beginning with red, then orange, and then blue.

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10-8 Permutations

You can use the Fundamental Counting Principle to find the number of permutations.

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10-8 Permutations

Mary, Rob, Carla, and Eli are lining up for lunch. In how many different ways can they line up for lunch?

Additional Example 2: Using the Fundamental Counting Principle to Find the Number of Permutations

There are 4 choices for the first position.There are 3 remaining choices for the second position.

There are 2 remaining choices for the third position.There is one choice left for the fourth position.

4 · 3 · 2 · 1 There are 24 different ways the students can line up for lunch.

Multiply.= 24

Once you fill a position, you have one less choice for the next position.

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10-8 Permutations

The Fundamental Counting Principle states that you can find the total number of outcomes by multiplying the number of outcomes for each separate experiment.

Remember!

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10-8 PermutationsCheck It Out: Example 2

How many different ways can you rearrange the letters in the name Sam?

There are 3 choices for the first position.There are 2 remaining choices for the second position.

There is one choice left for the third position. 3 · 2 · 1

There are 6 different ways the letters in the name Sam can be arranged.

Multiply.= 6

Once you fill a position, you have one less choice for the next position.

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10-8 Permutations

A factorial of a whole number is the product of all the whole numbers exceptzero that are less than or equal to the number.

“3 factorial” is 3! = 3 · 2 · 1 = 6

“6 factorial” is 6! = 6 · 5 · 4 · 3 · 2 · 1 = 720

You can use factorials to find the number of permutations.

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10-8 Permutations

How many different orders are possible for Shellie to line up 8 books on a shelf?

Additional Example 3: Using Factorials to Find the Number of Permutations

Number of permutations = 8!= 8 · 7 · 6 · 5 · 4 · 3 · 2 · 1

= 40,320There are 40,320 different ways for Shellie to lineup 8 books on the shelf.

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10-8 PermutationsCheck It Out: Example 3

How many different orders are possible for Sherman to line up 5 pictures on a desk?

Number of permutations = 5!= 5 · 4 · 3 · 2 · 1= 120

There are 120 different ways for Sherman to lineup 5 pictures on a desk.