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Math Help - Registration of cars

  1. #1
    Newbie bilalrouf's Avatar
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    Registration of cars

    there are 3 ways for the Registration of cars.

    1: ABC-123 or XYZ-123
    2: AB-1234 or YZ-1234
    3: A=13245 or Z-12345

    by which method maximun number of cars can be registred???

    Note: there should be no entry like this .
    ABC-000 or AB-0000 or A-00000
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  2. #2
    Newbie bilalrouf's Avatar
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    ..

    i think we can solve it by finding permutation of each part separately.like this

    ABC-123
    possible number of Registration ={ permutation of ABC }* {permutation of 123)
    = (26 P 3) * (10 P 3)
    = 15600 * 720
    = 11232000


    AB-1234
    possible number of registration = (26 P 2) * (10 P 4)
    = 650 * 151200
    = 98280000

    A-12345
    possible number of registration = (26 P 1) * 10 P 5
    = 26 * 30240
    = 786240

    answer is AB-1234
    is it correct to solve this problem in this way??
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  3. #3
    MHF Contributor

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    This problem is in need of clarification.
    It is not clear if you are allowing repetition?
    Can we have a tag such as ADD1322.
    You seem to allow repetition in that you say we cannot have AXY0000.
    Or is that letters cannot be repeated but digits can?

    All of your answers assume no repetitions.
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  4. #4
    Newbie bilalrouf's Avatar
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    ..

    if Repetation is allowed only in alphabet then what will be the answer
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by bilalrouf View Post



    AB-1234
    possible number of registration = (26 P 2) * (10 P 4)
    = 650 * 151200
    = 98280000
    A reality check on this shows that this cannot be right. Without any
    restriction on the registrations other that 2 alphas followed by 4 numerics
    gives 26^2*10^4 possible registrations ~= 6.8 million

    RonL
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by bilalrouf View Post
    if Repetation is allowed only in alphabet then what will be the answer
    Under almost any restrictions about repetitions AAA-NNN will give more
    registrations than the others just because there are so many more symbols
    that you can drop into the Alpha positions compared to the Numeric
    positions.

    RonL
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