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Thread: License Plates

  1. #1
    Silver Lounger
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    License Plates

    If a typical license plate is composed of three letters and three numbers in the format of the example: (ex. ABC - 123), how many unique plates can be produced?
    And Part Two... How many license plates can be formed if duplication of letters or numbers (on the same plate) is not allowed?

    Note: No funny-business here...We're using a 26-letter alphabet and the ten digits: 0,1,2,...
    - Ricky

  2. #2
    Plutonium Lounger
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    Re: License Plates

    Part 1: <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>26*26*26*10*10*10 = 17,576,000</font color=yellow></span hi>
    Part 2: <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>26*25*24*10*9*8 = 11,232,000</font color=yellow></span hi>

    StuartR

  3. #3
    Silver Lounger
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    Re: License Plates

    Exactly! <img src=/S/cheers.gif border=0 alt=cheers width=30 height=16>

    - When I first seen this puzzle, I knew how to solve the first part. But the second part, I didn't know where to begin. Still don't quite understand the reason your formula works but I know the end result is correct.
    - Ricky

  4. #4
    Plutonium Lounger
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    Re: License Plates

    Still don't quite understand the reason your formula works

    Consider the three letters.
    <span style="background-color: #FFFF00; color: #000000; font-weight: bold"><font color=yellow>The first one can be any of the 26 letters in the alphabet
    The second can be any of the 25 remaining letters
    The third can be any of the remaining 24</font color=yellow></span hi>
    Similarly for the 3 digits.

    StuartR

  5. #5
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    Re: License Plates

    <img src=/S/doh.gif border=0 alt=doh width=15 height=15> Thanks...makes perfect sense now.
    - Ricky

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