Serial numbers for a product are to made using 4 letters followed by 4 numbers. If the letters are t

Discussion in 'Calculator Requests' started by math_celebrity, Jun 14, 2017.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    Serial numbers for a product are to made using 4 letters followed by 4 numbers. If the letters are to be taken from the first 5 letters of the alphabet with repeats possible and the numbers are taken from the digits 0 through 9 with no repeats, how many serial numbers can be generated?

    First 5 letters of the alphabet are {A, B, C, D, E}

    The 4 letters can be chosen as possible:
    5 * 5 * 5 * 5

    The number are not repeatable, so the 4 numbers can be chosen as:
    10 * 9 * 8 * 7 since we have one less choice with each pick

    Grouping letters and numbers together, we have the following serial number combinations:
    5 * 5 * 5 * 5 * 10 * 9 * 8 * 7 = 3,150,000
     

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