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Section 12.7
Permutations and Combinations
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PermutationsAn arrangement or listing where
order is important.
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List the different ways can you arrange these characters?
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In how many different ways can you arrange these characters?
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Factorials
7! 10! 5!
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Travel The Flintstones will visit a complex of theme parks during their summer vacation. They have a four-day pass good at one park per day; they can choose from seven parks. How many different ways can they arrange their vacation schedule?
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How many five-digit numbers can be made from the digits 2, 4, 5, 8, and 9 if each digit is used only once?
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How many two-digit numbers can be made from the digits 2, 4, 5, 8, and 9 if each digit is used only once?
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Track and Field How many ways can six runners be arranged on a four-person relay team?
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List different teams of two can you choose from these characters.
Teams:
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Combinations
An arrangement or listing
where order is not important.
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Shirts How many ways can three shirts be selected from a display having a red shirt, a blue shirt, a green shirt, a black shirt, and a white shirt?
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Pens How many ways can a customer choose four pens from a blue, yellow, purple, orange, green, red, or black pen?
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Books How many ways can a student select 2 books from a bookshelf containing a mystery, a biography, a non-fiction book, a fantasy book, and a novel?
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If all of these characters shake hands, how many handshakes will take place?
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How to tell the difference between permutations and combinations:
Does order make a difference?
If yes, then it’s a permutation.
If no, then it’s a combination.
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Permutation or Combination?
How many ways can a 3-person team be chosen from 9 people?
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How many ways can 15 actors fill 6 roles in a play?
Permutation or Combination?
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A pizza shop has 12 toppings to choose from. How many different 3-topping pizzas can be ordered?
Permutation or Combination?
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Homework
P 644 10-29 all