7HW p.43 #22A caterer knows that, on average, there will be one broken egg in every 3 cartons. A carton contains 12 eggs. The caterer plans to serve 1200 eggs at a breakfast. What is the best estimate for the number of cartons the caterer should buy?97 cartons100 cartons103 cartons112 cartons
8HW p.44 #40Team A has won one game and team B has won three games in a World Series. What is the experimental probability that team A wins the next game? That team B wins the next game?Do you think that experimental probability is a good predictor of the winner of the next game? Explain.
96.7: Permutations & Combinations GOAL: Be able to apply permutations and combinations.
10BIGELOW’S PIZZERIAWelcome to Bigelow’s Pizzeria!! We offer 4 types of pizza and 8 different pizza toppings. As our star customer, you get to choose the toppings below.Pizza TypesPizza ToppingsCheeseWhiteThin CrustStuffed Crust
11BIGELOW’S PIZZERIAWait, seriously?? You want an 8-slice cheese pizza with a different topping on each slice? Write your toppings into each slice the way you want them arranged:If the positioning of the toppings on the slices doesn’t matter, how many ways can you choose 8 toppings out of the 8 toppings?If the positioning of the toppings on the slices does matter, how many ways can you arrange the 8 toppings on the slices?
12Permutations!A permutation is an arrangement of items in a particular order!
13Permutations!n! means n factorial, multiplying by every positive integer from 1 to n
14Example 1!Trophies!In how many ways can you arrange six trophies on a shelf?!
15Example 2!Dogs!In how many orders can ten dogs line up to be groomed?!
16Permutations!Above, we have been focusing on the order of every object given! We won’t always! The number of permutations of n items of a set arranged r times at a time is nPr𝑛 𝑃 𝑟 = 𝑛! 𝑛−𝑟 ! for 0≤𝑟≤𝑛
17Example 3!Boat Race!Seven boats enter a race! First, second, and third places will be given to the three fastest boats! How many arrangements of first, second, and third places are possible with seven boats?! With ten boats?!
18Example 4!Pizza SlicesYour pizza’s ready! You want to share your custom pizza with 3 friends! The four of you each take one slice! How many possibilities are there for the toppings that all four of you end up eating?! What if there were five of you?!
19CombinationsA selection r of n total objects in which order does not matter is a combination𝑛 𝐶 𝑟 = 𝑛! 𝑟! 𝑛−𝑟 ! for 0≤𝑟≤𝑛