6.7 Permutations and Combinations. Fundamental Counting You have the following clothes to choose from: 1 black and1 blue pair of jeans 1 yellow, 1 green,

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Presentation transcript:

6.7 Permutations and Combinations

Fundamental Counting You have the following clothes to choose from: 1 black and1 blue pair of jeans 1 yellow, 1 green, 1 red t-shirt How many different outfits can you make?

Fundamental Counting You are taking a multiple-choice test that has 10 questions and each question has 4 answer choices. How many possible ways are there to answer all 10 questions?

Fundamental Counting Telephone numbers in the U.S. begin with a 3-digit area code, followed by seven-digit local number. Area codes and local numbers cannot begin with 0 or 1 How many different telephone numbers are there? By the year 2020, the US population is expected to be 323 million. Are we going to run out of phone numbers?

Permutations – an ordered arrangement of items No item is used more than once Order matters Permutation Formula: No item is used more than once Order matters Permutation Formula:

Permutations Ex3) Jon, Emily, Dan, Megan, and Annie are running for student council. The offices are President, Vice President, and Secretary. How many ways can these five students fill the positions? PresidentVice PresidentSecretary JEDMAJEDMA Notice that we can accomplish the same thing using the Multiplication Counting Principle!

No item is used more than once Order does NOT matters Combination Formula: No item is used more than once Order does NOT matters Combination Formula: Combinations Divides out combinations that are the same items in a different order Example: A pasta bar offers 6 different add-ins. How many ways can you choose 4 add-ins for your pasta? Does the order matter?

Permutation or Combination? 1. You have 7 different textbooks: Latin, French, History, Geography, Math, Physics, and Chemistry. How many different ways can you arrange them on your shelf in your bedroom? 2. In poker, a person is dealt 5 cards from a standard 52-card deck. The order does not matter? How many different 5-card poker hans are possible? 3. You have 6 friends. How many ways can you choose 4 of them to hang out with you? 4. How many ways can you turn up 3 cards in order from a deck of 52 cards?