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If a license plate has 3 letters and then 3 numbers, what are the chances (probability?) of getting at least 1 letter "Z" in one of the letter spots if the letters are picked randomly?
and I think each letter can only be used once.

  • Math -

    when you say, "at least 1 letter "Z" in one of the letter spots", you are implying that there could be 1,2, or 3 Z's in the letter spots.
    But then you say that you think each letter can be used only once.

    Usually on license plates, letters and numbers can be repeated, so I will work it out assuming that both letters and numbers can be repeated.

    case 1: one Z
    number of ways = 3x25x25x1000 = 1875000
    case 2: two Z's
    number of ways = 3x25x1000 = 75000
    case 3: three Z's
    number of ways = 1x1000 = 1000
    total number of ways to have Z's = 1951000

    number of ways without restrictions = 26x26x26x1000 = 17576000

    so prob of at least 1 Z = 1951000/17576000 = ..111

    other way:
    no Z's at all = 25x25x25x1000 = 15625000
    so number of ways for at least one Z
    = 17576000 - 15625000 = 1951000

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