Permutations and Combinations Random Things to Know Random

Permutations and Combinations

Random Things to Know •

Random Things to Know Cards Typical Deck: 52 cards 4 Suits (13 cards each) Clubs 2 -10 3 Face 1 Ace Spades 2 -10 3 Face 1 Ace Hearts 2 -10 3 Face 1 Ace Diamonds 2 -10 3 Face 1 Ace

Random Things to Know

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

Counting Principle •

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 _____. Ex 1: Ex 2: 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

Permutations • You can use your calculator to find permutations • To find the number of permutations of 10 items taken 6 at a time (10 P 6): • Type the total number of items • Go to the MATH menu and arrow over to PRB • Choose option 2: n. Pr • 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 •

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 •

Combinations • You can use your calculator to find combinations • To find the number of combinations of 10 items taken 6 at a time (10 C 6): • Type the total number of items • Go to the MATH menu and arrow over to PRB • Choose option 3: n. Cr • 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: _______