Find the number of Find the number of outcomesoutcomes

1)1) At a pizza place you can order At a pizza place you can order thin or thick crust, one meat thin or thick crust, one meat topping (sausage, pepperoni, topping (sausage, pepperoni, ham), and one vegi (onions, ham), and one vegi (onions, mushrooms, olives, or peppers). mushrooms, olives, or peppers). How many pizzas possible?How many pizzas possible?

2)2) What are the chances of picking What are the chances of picking a thin crust, pepperoni, and a thin crust, pepperoni, and onion pizza?onion pizza?

How many outcomes?How many outcomes?

1)1) A coin is flipped 5 times. How many A coin is flipped 5 times. How many possible outcomes?possible outcomes?

2)2) Picking 4 cards from a deck of cards? Picking 4 cards from a deck of cards?

3)3) Make a 3 number lock combination Make a 3 number lock combination from numbers 0-20 (repeating from numbers 0-20 (repeating permitted)? permitted)?

4)4) Rolling an 8-sided number cube and Rolling an 8-sided number cube and flipping a coin? flipping a coin?

How many outcomes?How many outcomes?

In your class elections, Ty and Sue are In your class elections, Ty and Sue are running for president, Frank and Li running for president, Frank and Li are running for vice-president, are running for vice-president, Andrew, Jerry and Paige are running Andrew, Jerry and Paige are running for treasurer, and Matt and Keesha for treasurer, and Matt and Keesha are running for secretary. How many are running for secretary. How many different election results are different election results are possible?possible?

Find the number for each Find the number for each PermutationPermutation

1)1) 1616PP88

2)2) 99PP99

3)3) 77PP22

4)4) 88PP33

5)5) 1010PP11

Answers to PermutationsAnswers to Permutations

1)1) 518,918,400518,918,400

2)2) 362,880362,880

3)3) 4242

4)4) 336336

5)5) 1010

Bookstore problem Bookstore problem

A bookstore you work at is having employee A bookstore you work at is having employee favorites on display. Each employee favorites on display. Each employee displays 3 of his or her favorite books. To displays 3 of his or her favorite books. To help you decide, you make a list of your 12 help you decide, you make a list of your 12 favorite books. In how many ways can you favorite books. In how many ways can you choose 3 books?choose 3 books?

Does order matter?Does order matter?

Bookstore problemBookstore problem

You can choose 3 out of the 12. You can choose 3 out of the 12.

________ * _______ * ________.________ * _______ * ________.

However, order does not matter so your answer However, order does not matter so your answer is less than a permutation. Divide by the is less than a permutation. Divide by the factorial number of blanks you would fill infactorial number of blanks you would fill in

12 * 11 * 10 12 * 11 * 10 = = 1320 1320 = 220= 220

3 * 2 * 1 63 * 2 * 1 6

CombinationsCombinations►Number of combinations of r objects Number of combinations of r objects

taken from a group of n distinct objects taken from a group of n distinct objects ►Order does not matterOrder does not matter

nnCCrr = = n! n! (n-r)!*r!(n-r)!*r!

1212CC33 = = 12 ! 12 ! = = 12 * 11 * 10 * 9 !12 * 11 * 10 * 9 ! 9! * 3!9! * 3! 9 ! * 3 * 2 * 19 ! * 3 * 2 * 1

Combinations – Find eachCombinations – Find each

1)1) How many ways can you choose 4 How many ways can you choose 4 kinds of fish from 26 kinds at a pet kinds of fish from 26 kinds at a pet store?store?

2)2) How many ways can you choose 2 How many ways can you choose 2 DVDs from 31 DVDs in the new DVDs from 31 DVDs in the new release section at the movie store?release section at the movie store?

3)3) How many ways can you choose 3 How many ways can you choose 3 toppings for a pizza from 18 available toppings for a pizza from 18 available toppings?toppings?

Combinations – how many?Combinations – how many?

1)1) A track team of 120 members can A track team of 120 members can choose 3 co-captains?choose 3 co-captains?

2)2) Choose 2 toppings for your ice cream Choose 2 toppings for your ice cream from 12 available?from 12 available?

3)3) Choose 5 color combination from 12 Choose 5 color combination from 12 colors?colors?

4)4) Choose 4 girls from a class of 24 Choose 4 girls from a class of 24 girls?girls?