Permutations and Combinations. Random Things to Know.

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Permutations and Combinations

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Presentation transcript:

Permutations and Combinations

Random Things to Know

Cards Typical Deck: 52 cards 4 Suits (13 cards each) Clubs Spades2-103 Face1 Ace HeartsDiamonds2-103 Face1 Ace

Random Things to Know

Counting Principle If you have 6 shirts and 3 pants how many different outfits can you create?

Counting Principle

When flipping a coin 15 times how many results are possible? *Think how many different results are there when you flip a coin* _________________

Counting Principle A restaurant has on its menu 5 choices for appetizers 3 choices for main course 2 choices for dessert How many different meals (appetizer, main course, and dessert) can you choose? _____________________

Factorials Many equations in probability use ____________. A ____________ is a mathematical concept that is represented by an _____. Ex1: Ex2: To do a factorial in the calculator: ________________________________

Let’s Practice…… A student is to roll a die and flip a coin. How many possible outcomes will there be? Answer: _________ For a college interview, Robert has to choose what to wear from the following: 4 slacks, 3 shirts, 2 shoes and 5 ties. How many possible outfits does he have to choose from? Answer:__________

Permutations You and your 3 friends are standing in line to buy tickets to a movie. How many ways are there for you to arrange yourselves?

Permutations Remember the Counting Principle: M*N = total number of ways to select items How many choices do you have for the first spot?___ How many choices do you have for the second spot?__ How many choices do you have for the third spot?___ How many choices do you have for the fourth spot?__ So________________________

Permutations Def:_______________________________ __________________________________ In races who comes in 1 st, 2 nd, and 3 rd is very important for prizes, and rankings. The order does matter.

Permutations

You can use your calculator to find permutations To find the number of permutations of 10 items taken 6 at a time (10P6): Type the total number of items Go to the MATH menu and arrow over to PRB Choose option 2: nPr Type the number of items you want to order

Let’s Practice…… Find the number of ways to arrange the letters ABC. Answer:_______ A combination lock will open when the right choice of three numbers (from 1 to 30, inclusive) is selected. How many different lock combinations are possible assuming no number is repeated? Answer:_______

Combinations If you have 5 trophies but only space on a shelf for 2 of them how many different ways can you arrange your trophies? BIG QUESTION: DOES ORDER MATTER??

Combinations

Def:______________________________________ _________________________________ If you order pizza it doesn’t matter if you tell them “Peperoni, Pineapple, and Sausage” or “Sausage, Peperoni, and Pineapple” NO! It all goes on the pizza! ___________________________

Combinations

You can use your calculator to find combinations To find the number of combinations of 10 items taken 6 at a time (10C6): Type the total number of items Go to the MATH menu and arrow over to PRB Choose option 3: nCr Type the number of items you want to order

Let’s Practice…… To play a particular card game, each player is dealt five cards from a standard deck of 52 cards. How many different hands are possible? Answer:_______ A basketball team consists of two centers, five forwards, and four guards. In how many ways can the coach select a starting line up of one center, two forwards, and two guards? Answer:_______