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.
10-8 Permutations
Vocabularypermutationfactorial
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.
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
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.
10-8 Permutations
You can use the Fundamental Counting Principle to find the number of permutations.
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.
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!
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.
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.
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.
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.
