Chapter 13 Goal: 1.03 Use theoretical and experimental probability to model and solve problems. a) Use addition and multiplication principles. b) Calculate and apply permutations and combinations. The student will be able to: 1.Solve problems related to the Basic Counting Principle. 2.Distinguish between dependent and independent events. 3.Solve problems involving permutations or combinations.

Ivette is a freshman at the University of Miami. She is planning her schedule for next school year. She has a choice of three mathematics courses, two science courses, and two humanities courses. She can only select one course from each area. How many course schedules are possible? Does her choice of math course affect her choice of science class? No, so these three choices are all independent events. Events that do affect each other are called dependent events. Finding different possibilities for the arrangement of objects is called combinatorics. **If one event can be chosen in p different ways and another independent event can be chosen in q different ways, then the two events can be chosen successively in p x q different ways. ** Since Ivette has 3 math courses, 2 science courses, and 2 humanities courses, she has 3 x 2 x 2 (or 12) different ways to schedule her class. Section 1: Permutations and Combinations

Vickie works for a bookstore. Her manager asked her to arrange a set of five best-sellers for a display. The display is to be set up as shown below. The display set is made up of one book from each of 5 categories. There are 4 nonfiction, 4 science fiction, 3 history, 3 romance, and 4 mystery books from which to choose. Nonfictio n Science Fiction HistoryRomanceMystery 1 st spot2 nd spot 3 rd spot 4 th spot5 th spot Are the choices for each spot independent or dependent of each other? How many different ways can Vickie choose the books for the display?

Mr. Casey has decided to buy a new suit made either of wool or rayon. He has narrowed down the choices of available colors to gray, blue, black, or tan, and the matching tie to a floral, a stripe, or a geometric pattern. a.Assuming that all choices make an acceptable appearance, are the choices for material, color, and tie pattern independent or dependent events? b.How man different selections of his suit and tie are possible? Permutations is an arrangement of objects in a certain order. The order the objects are take is important. The number of permutations of n objects taken n at a time is defined as P(n, n)= n!

Ex: During a judging of a horse show at the Fairfield County Fair, there are three favorite horses: Rye Man, Oiler, and Sea of Gus. a.Are the selection of first, second, and third place from the three horses independent or dependent events? b.Assuming there are no ties and the three favorites finish in the top three places, how many ways can the horses win first, second, and third places. A math teacher needs to place five books-algebra, algebra 2, geometry, trigonometry, and advanced math- on her bookshelf. Assume that all of the books are placed upright with the binded edges in view. a.Is the process of placing the books on the shelf a series of independent or dependent events? b.How many ways can the books be displayed on the shelf?

The board of directors of BELA Technology Consultants is composed of 10 members. a.How many different ways can all the members sit at the conference table? b.In how many ways can they elect a chairperson, vice-chairperson, treasurer, and secretary, assuming that one person cannot hold more than one office? A high school honor society is composed of 7 students. a.How many ways can all the members stand in a straight line for a picture? b.In how many ways can they select a president and a vice-president, assuming that one person cannot hold more than one office?