Math

Emil is shopping for a convertible. He plans to test drive three cars, a Toyota, a Honda, and a Mazda. He also wants to test drive both the 5-speed standard and the automatic transmission in each, but the Mazda isn't made with an automatic transmission. He would like to test drive the cars both with the trunks empty and with the trunks fully loaded to see how they perform, but the Toyota doesn't have a trunk. How many test drives he will have to do to check all the combination of features?

I came up with 29 because with the Honda you can test all 4 things and then you can arrange those 4 things in a different order to get 16. Then with a Toyota you can only test 2 thigs and then arrange those 2 things in a different order to get 4. Finally, with the Mazda you can test 3 things and then you can arrange those 3 things in different orders to get 9.

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  1. I come up with 8.

    Toyota: 2 options: 5-speed or automatic (both with no trunk)
    Mazda: 2 options:
    5-speed w/trunk loaded;
    5-speed w/trunk empty
    Honda: 4 options:
    5-speed w/trunk loaded
    5-speed w/trunk empty
    automatic w/trunk loaded
    automatic w/trunk empty

    I lost you when you mentioned "all four things" and "in different orders"

    The order of what you test is no important.

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