15 1 Permutations Brett Solberg AHS 11 12

+ 15. 1 Permutations Brett Solberg AHS ‘ 11 -’ 12

+ Warm-up n

+ Today’s Agenda n Probability n Compound Events n Permutations n n Combinations n n Ordered probability Unordered Probability CRT Checklist n calculator n book n pencil

+ Texas Roadhouse n Steak + Salad + Side n Steak Salad Side 6 oz 8 oz 10 oz House Caesar Baked Potato Fries Chili n n Event n n Outcome n n Dinner What I eat How many different outcomes are there?

+ Fundamental Counting Principle n The total number of outcomes is all of the possibilities for each event multiplied together. n Steak + Salad + Side n 3 * 2 * 4 n 24 total outcomes

+ What to wear? n Jani can choose gray or blue jeans, a navy, white, green, or striped shirt, and running shoes, boots, or penny loafers. How many outfits can she wear? n Pants + shirt + shoes

+ Pizza n A restaurant offers four sizes of pizza, two types of crust, and eight toppings. How many combinations with one topping are there? n Size + crust + topping

+ Factorials! n A number multiplied by all numbers less than it. n 5! = 5*4*3*2*1 n 9! n 0! n a!

+ Permutations n

+ Examples n In how many ways can six circus elephants be arranged in a line? n In how many ways can the four symbols *, !, @, # be arranged?

+ Examples n In how many ways can one write three letters on a tag using the letter A, B, C, D, and E at most once. n A teacher wants to write an ordered 6 -questions test from a pool of 10 questions. How many different forms of the test can the teacher write?

+ Examples n How many 7 -digit numbers can be named, without repetition, using the digits 2, 3, 4, 5, 6, 7, and 8 if an even digit must come first.

+ Combination n Deals with ways of selecting from a set. n How many combinations are there of the set {A, B, C, D} taken two at a time? n {A, B} {A, C} {A, D} {B, C} {B, D} {C, D} n How is this different from a permutation? n Combination - selection is important, not order.

+ Combination n

+ Combinations n

+ Combination Examples n In how many ways can a 5 -player starting unit be selected from Alta’s 12 member basketball squad?

+ Combination Example n In how many ways can a starting 11 unit be chosen from RSL’s 26 person roster?

+ Combination Example n In how many ways can a committee of 3 be chosen from a group of 7 people?

+ n You want to ride the following rides at Lagoon but only have time to ride 4. How many possibilities are there? n Samurai n Colossus n Bombora n Jet Star 2 n Rocket n Rattlesnake Rapids

+ Assignments n 15. 1 1 – 39 odd n 15. 3 1 – 15 all