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What is the probability of getting a license plate that has a repeated letter or digit if you live in a state that has three numerals followed by five letters followed by one numeral? (Round to the nearest whole percent.)

  • algebra -

    number of all possible plates
    =10^3 * 26^5 * 10
    = 118813760000 (this includes all types of repetition)
    number of plates without any repetition
    = 10*9*8*26*25*24*23*22*7
    3.9783744 x 10^10

    so prob of some kind of repeat
    = 1 - 3.9783744 x 10^10/118813760000
    = .665

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