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  1. #1
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    data staff.`.`.`.`

    In how many possible ways can a family of five be seated in a passenger car if either two or three people sit in the front seat and only tow members can drive? (ps : as my understanding, totally the can contained 6 seats, 3 in front, and 3 in the back)

    Please leave your solutions as well.... thank u very much
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  2. #2
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    Quote Originally Posted by ives View Post
    In how many possible ways can a family of five be seated in a passenger car if either two or three people sit in the front seat and only tow members can drive? (ps : as my understanding, totally the can contained 6 seats, 3 in front, and 3 in the back)

    Please leave your solutions as well.... thank u very much
    Let's do some surgery and disect this problem!

    Two different people can drive, so this gives us two possibilities. Of those two possibilities, there are $\displaystyle 4!$ different ways you can arrange the other four people. This applies to Person A and Person B, so we have $\displaystyle 2*4!$ ways that the family can be arranged. Lastly, we can have two or three people in the front, so this once again doubles out possibilities to give us a final answer of $\displaystyle 4*4! = 96$ arrangements.

    Let me know if I missed anything!
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