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# Counting techniques

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Combine algebraic sets to yield other sets, understand techniques for determining the number of elements in a set, and use permutations and combinations formulas to combine or arrange elements in a set.

II. The three different media outlets of radio, Internet, and newspaper are to be offered on weekends or weekdays, and then either between 7 a.m.-3 p.m., 3 p.m.-11 p.m. or 11 p.m.-7 a.m. How many different possibilities exist? List the possibilities and verify your listing with the multiplication principle for counting.

III. Suppose that your boss has decided that he wants to do a variety of three different groupings based from problem II. For example, one grouping might be (Radio-Weekday-7 a.m., Internet-Weekend-11 p.m., Newspaper-Weekday-3 p.m.). Explain to your boss how many varieties he has to choose from and how you arrived at this value.

IV. After seeing the many ways that your boss has to choose from part III, you have decided to put together a team to examine these possibilities. The team will consist of a team leader, advertising expert, and a mathematician. The first person chosen on the team will be the team leader, second will be the advertising expert, and the third will be the mathematician. You have narrowed down your choices to Chris, Bob, and Sally. List the different ways that you can put together this team of experts. Does the order of the members matter? Explain.

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