Math probability

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How many ways can three cars be parked in a row of four parking spaces?

I have no idea how to do this?

  • Math probability -

    Can they be facing in or out? Or do they have to drive head in?

    Let's assume the latter.

    The first car has four spaces to choose from. That leaves the second car with three choices and the third with two. Take the product:
    4 x 3 x 2 = ?

  • Math probability -

    Well, you are actually parking three cars and an empty space.

    What is 4!
    Let cars be aBC and E is the empty space
    EABC
    EACB
    EBCA
    EBAC
    ECAB
    ECBA
    then you can move the E to the other three positions, you will get six in each, or 24 total, or 4!

  • Math probability -

    and, I forgot the headin/headout that DrWLS mentioned.
    That makes the 4! now 4!*2*2*2

  • Math probability -

    4 x 3 x 2 = 24

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