Radar detectors are either powered by their own battery or plug into the cigaret

Question

Radar detectors are either powered by their own battery or plug into the cigarette lighter socket. All radar detectors come in two models: no-frills and fancy. In addition, detectors powered by their own batteries detect either radar or laser, or both, whereas the plug-in types come in models that detect either radar or laser, but not both. How many different radar detectors can you buy?
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Professor Easy's final examination has 14 true-false questions followed by 2 multiple-choice questions. In each of the multiple-choice questions, you must select the correct answer from a list of six. How many answer sheets are possible?
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The local diner offers a meal combination consisting of an appetizer, a soup, a main course, and a dessert. There are four appetizers, four soups, five main courses, andfour desserts. Your diet restricts you to choosing between a dessert and an appetizer. (You cannot have both.) Given this restriction, how many three-course meals are possible?
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Explanation / Answer

1)

number of plug-in types: 2*2 = 4

number of power by itself radars: 2*3 = 6

total number = 4+6 = 10

2)

2*2*...*2 * 6*6 = 2^14 * 6^2 = 589824

3)

number of meals with appetizer: 4*4*5 = 80

number of meals with dessert: 4*5*4 = 80

total number = 80 + 80 = 160

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