Do Now Suppose Shaina’s coach has 4 players in mind for the first 4 spots in the lineup. Determine the number of ways to arrange the first four batters.

HW KEY (Pg #1- 8, 19-31) 1)Dependent, 28/253 or about 11% 2)Dependent, 3/38 or about 8% 3)Independent, 4/9 or about 44% 4)Independent, 64/289 or about 22% 5)Mutually exclusive; 2/13 or about 15% 6)Mutually exclusive; ½ or about 50% 7)Not mutually exclusive; 4/13 or about 31% 8)Not mutually exclusive; 4/13 or about 31% 19) P(red, blue) = 8/87 or about 9% 20) P(blue, yellow) = 16/145 or about 11% 21) P(yellow, not blue) = 42/145 or a bout 29% 22) P(red, not yellow) = 17/87 or about 20% 23) P(white, white) = 91/276 or about 33% 24) P(heart or spade) = ½ or 50% 25) P(spade or club) = ½ or about 50% 26) P(queen, then heart) = 4/221 or about 2% 27) P(jack, then spade) = 4/221 or about 2% 28) P(five, then red) = 25/663 or about 4% 29) P(ace or black) = 7/13 or about 54% 30) P(red, red, orange) = 125/5488 or about 2% 31) a) 345 b) 159 c) 227/345 or about 66% d) 2/23 or about 9%

Permutations and Combinations

Sample Space The list of all of the choices in a group. o When the objects are arranged so that the order is important and every possible order of the objects is provided, the arrangement is called a permutation. o When the order is not important, it is called a combination.

Why? The list shows the classes you plan to take next year. You wonder how many different ways there are to arrange your schedule for the first three periods of the day. a.Make a tree diagram that lists all of the possibilities for the three periods. Do not repeat any classes in each arrangement. b.How many different choices did you have for the first period? The second period? The third period? Scheduling Options Algebra Biology Language Arts Spanish World History Scheduling Options Algebra Biology Language Arts Spanish World History

Definition Permutation: an arrangement or listing in which order is important Notation - P(5,3) represents 5 things, taken 3 at a time. Formula – P(n,r ) = n!/(n-r)!

Example 1 The librarian is placing 6 of 10 magazines on a shelf in a showcase. How many ways can she arrange the magazines in the case?

Practice A designer has created 15 outfits and needs to select 10 for a fashion show. How many ways can the design arrange the outfits for the show? Four of ten different fruits are being selected to be placed in a row in a display window. In how many ways can they be placed?

Example 2 How many zip codes can be made from the digits 0, 7, 5, 4, and 6 if each digit is used only once?

Definition Sometimes order doesn’t matter! Example: chocolate, vanilla, and strawberry is the same as strawberry, chocolate, and vanilla when you order ice cream. Combination: an arrangement or listing where order is not important Notation - C(5,3) represents 5 things, taken 3 at a time where the order does not matter. Formula – C(n, r) = n!/[(n-r)!r!]

Example 3 How many ways can students choose two flavors of sherbet from orange, lemon, strawberry, and raspberry?

Lucas works part-time at a local department store. His manager asked him to choose for display 5 different styles of shirts from the wall of the store that has 8 shirts on it to put in a display. How many ways can Lucas choose the shirts?

Practice In how many ways can you choose two student council representatives from the students shown? Jack, Joey, Adra, Aidan, Bryan How many ways can a customer choose 3 pizza toppings from pepperoni, onion, sausage, green pepper, and mushroom?

Example 4 A combination lock requires a three-digit code made up of the digits 0 through 9. No number can be used more than once. o How many different arrangements are possible? o What is the probability that all of the digits are odd?

Practice The Spanish club is electing a president, vice president, secretary, and treasurer. Rebekah and Lydia are among the nine students who are running. o How many ways can the Spanish club choose their officers? o Assuming that the positions are chosen at random, what is the probability that either Rebekah or Lydia will be chosen as president or vice president?

Homework Pg #9, 10, 11, 14, 18, All