13.1 Permutations and Combinations Solve problems related to the Basic Counting Principle. Distinguish between dependent and independent events. Solve.

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Presentation transcript:

13.1 Permutations and Combinations Solve problems related to the Basic Counting Principle. Distinguish between dependent and independent events. Solve problems involving permutations or combinations.

Suppose you flip three coins (a penny, a nickel and a dime), how many possible outcomes exist? Multiple Events/Categories Tree Diagram Each category is represented by a branch of the tree. Follow the branches to determine all of the outcomes. Basic Counting Principle Suppose 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 pq ways.

1) 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)How many different selections of his suit and tie are possible? 2) Kenny bought a new 3-number lock combination in which he can make his own combination. a)How many possible combinations could he make if numbers can repeat? b)How many possible combination could he make if every number must be different?

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. The are 4 nonfiction, 4 science fiction, 3 history, 3 romance and 3 mystery books from which to choose. NonfictionScience fictionHistoryRomanceMystery a)How many different ways can Vickie choose the books for the display?

Single Event scenarios Independent events Option A does not affect the choices in option B. Usually uses combination Dependent events Option A affects the choices in option B. Usually uses permutation

1) 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) Independent or Dependent events? b) How many ways can the books be displayed on the shelf? 2) Every year a popular magazine picks the 15 top-rated television movies of the previous year. A network wants to select 3 out of these 15 movies to show during the month of August. How many groups of 3 movies can be selected?

3) A high school honor society is composed of 7 students. a)How many different 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 that one office?

4) The US Postal Service uses 5-digit ZIP codes to route letters and packages to their destinations. a)How many ZIP codes are possible if the numbers 0 through 9 are used for each of the 5 digits? b)Suppose that when the first digit is 0, the second, third, and fourth digits cannot be 0. How many 5-digit ZIP codes are possible if the first digit is 0? c)In 1983, the U.S. Postal Service introduced the ZIP + 4, which added 4 more digits to the existing 5-digit ZIP codes. Using the numbers 0 through 9, how many additional ZIP codes were possible?