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Math Help - probability

  1. #1
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    probability

    A state has a license plate that is 3 letters followed by 4 digits. I and O cannot be letters, and the number 0 cannot be in the first space for the digits.

    A) How many different license plates are possible?

    B) If there are 3,000,000 vehicles in this state, how many license plates are still avaible for use after the current vehicle is licensed? (Don't worry about personalized licenses, etc.)
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  2. #2
    MHF Contributor arbolis's Avatar
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    a)For the first letter in the license plate, it can be one of 24 letters since there are 26 letters in the English alphabet and I and O cannot be chosen. Same for the 3 next letters. The first digit can be one of 9, the second and the lasts can be one of out 10. Therefore the result is 24^3*9*10^3=124,416,000.
    b) 124,416,000-3,000,000=121,416,000
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