Ex. 2 How Many Ways Can 4 Vases Be Arranged on a Shelf?

11-1 Notes Permutations and Combinations Fundamental Counting Principle – If there are “m” ways to do event 1 and “n” ways to do event 2, then there are ______ways to do event 1 followed by eventSame 2. concept for more than 2 events.

Ex. 1 to make a yogurt parfait, you choose a flavor of yogurt, a fruit topping, and a nut topping. If there are 2 flavors of yogurt, 5 fruit toppings, and 3 nut toppings, how many parfait choices are there?

Ex. 2 How many ways can 4 vases be arranged on a shelf?

Factorial (!) – the product of all positive integers from the given integer down to 1. e.g. 4! = 4 ∙ 3 ∙ 2 ∙ 1 = 6! =

It is often used to find the number of ways to arrange/order a set number of items. Calculator Note: To find ! in calculator, look under probability menu. Ex. 3 Find each. a) 9! b) 7! n! Permutations (nPr) = (n  r)! - used to find the number of ways to arrange a portion of a set number of items. Ex. 4 In a race there are 8 runners. How many ways can they come in 1st, 2nd, and 3rd place?

n! Combinations (nCr) = r!(n  r)! - used to find the number of ways of picking a portion of a group. Order does not matter! Ex. 3 There are 12 different colored marbles in a bag. How many ways can Randall draw a set of 4 marbles from the bag?

Day 1 Assignment w/s 11-1

Day 2 Show nPr and nCr in calculator Day 2 Assignment p. 798 #9-29, 39, 40