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28 March, 11:35

A twenty-something single person is planning a ski vacation. Assume that she has 3 possible destinations: New England, Utah, and Oregon. There are 3 ski areas in New England with 2 available times for 2 of the areas, and 3 times for the other area. There are 4 ski areas in Utah with 4 available times for 3 of the areas, and 3 times for the other area. There are 4 ski areas in Oregon with 4 available times for 3 of the areas, and 3 times for the other area. (A "time" refers to a weekend for which there are vacancies at the ski lodge.) A trip plan involves the selection of a location, ski area, and a time. How many possible plans are there?

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  1. 28 March, 13:43
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    Number of a trip plans:

    1) New England: 2 * 2 + 1 * 3 = 4 + 3 = 7

    2) Utah: 3 * 4 + 1 * 3 = 12 + 3 = 15

    3) Oregon: 3 * 4 + 1 * 3 = 12 + 3 = 15

    In total: 7 + 15 + 15 = 37

    Answer: There are 37 possible trip plans.
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