1. Find the number of outcomes 1) At a pizza place you can order thin or thick crust, one meat topping (sausage, pepperoni, ham), and one vegi (onions, mushrooms, olives, or peppers). How many pizzas possible? 2) What are the chances of picking a thin crust, pepperoni, and onion pizza?

2. How many outcomes? 1) A coin is flipped 5 times. How many possible outcomes? 2) Picking 4 cards from a deck of cards? 3) Make a 3 number lock combination from numbers 0-20 (repeating permitted)? 4) Rolling an 8-sided number cube and flipping a coin?

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

4. Find the number for each Permutation 1) 16 P 8 2) 9 P 9 3) 7 P 2 4) 8 P 3 5) 10 P 1

5. Answers to Permutations 1) 518,918,400 2) 362,880 3) 42 4) 336 5) 10

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

7. Bookstore problem You can choose 3 out of the 12. ________ * _______ * ________. However, order does not matter so your answer is less than a permutation. Divide by the factorial number of blanks you would fill in 12 * 11 * 10 = 1320 = 220 3 * 2 * 1 6

8. Combinations ► Number of combinations of r objects taken from a group of n distinct objects ► Order does not matter n C r = n! (n-r)!*r! 12 C 3 = 12 != 12 * 11 * 10 * 9 ! 9! * 3!9 ! * 3 * 2 * 1 9! * 3!9 ! * 3 * 2 * 1

9. Combinations – Find each 1) How many ways can you choose 4 kinds of fish from 26 kinds at a pet store? 2) How many ways can you choose 2 DVDs from 31 DVDs in the new release section at the movie store? 3) How many ways can you choose 3 toppings for a pizza from 18 available toppings?

10. Combinations – how many? 1) A track team of 120 members can choose 3 co-captains? 2) Choose 2 toppings for your ice cream from 12 available? 3) Choose 5 color combination from 12 colors? 4) Choose 4 girls from a class of 24 girls?