# HW1 - Lab 8 Key 1.1 and 1.2(page 11 1 During a local...

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Lab 8 Key 1.1 and 1.2 (page 11) 1. During a local campaign, eight Republican and five Democratic candidates are nominated for president of the school board. a) If the president is to be one of these candidates, how many possibilities are there for the eventual winner? 8 + 5 = 13 b) How many possibilities exist for a pair of candidates (one from each party) to oppose each other for the eventual election. 5 * 8 = 40 c) Which counting principle is used in part a) and in part b) . a) Rule of sum b) Rule of product 3. Buick automobiles come in four models, 12 colors, three engine sizes, and two transmissions types. a) How many distinct Buicks can be manufactured? 4 * 12 * 3 * 2 = 288 b) If one of the available colors is blue, how many different blue Buicks can be manufactured? 4 * 3 * 2 = 24 5. While on a Saturday shopping spree Jennifer and Tiffany witnessed two men driving away from the front of a jewelry shop, just before a burglar alarm started to sound. Although everything happened rather quickly, when the two ladies were questioned, they were able to give the police the following information about the license plate (Consisting of two letters followed by four digits) on the get-away car. Tiffany was sure that the second letter on the plate was either an O or a Q and the last digit was a 3 or an 8. Jennifer told the investigator that the first letter on the plate was either a C or a G and that 1

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the first digit was definitely a 7. How many different license plates will the police have to check? 1 st Letter: 2 choices 2 nd Letter: 2 choices 1 st Digit: 1 choice 2 nd Digit: 10 choices 3 rd Digit: 10 choices 4 th Digit: 2 choices 2 3 * 10 2 = 800 7. A certain “Burger Joint” advertises that a customer can have his or her hamburger with or without any or all of the following: catsup, mustard, mayonnaise, lettuce, tomato, onion, pickle, cheese, or mushrooms. How many different kinds of hamburger orders are possible? For each addition, you have two choices, include it or not. 9 additions = 2 9 13. a) How many permutations are there for the eight letters a, c, f, g, i, t, w, x? P (8, 8) = 8! b) Consider the permutations in part a). How many start with the letter t? How many start with the letter t and end with the letter c? Since t, is already placed in the beginning, we have 7 more letters to choose from. 7! If we place c at the end, the we only have 6 letters to choose from. 6!
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HW1 - Lab 8 Key 1.1 and 1.2(page 11 1 During a local...

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