ALGEBRA

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Many states offer personalized license plates. California, for example, allows personalized plates with seven spaces for numerals or letters, or one of the following four symbols. What is the total number of license plates possible using this counting scheme? (Assume that each available space is occupied by a numeral, letter, symbol, or space. Give the answer in scientific notation. Round the first number to two decimal places.)
The answer I came up with is 163840000000 x10 ~1.64E11 is this correct if not please help.

  • ALGEBRA -

    I counted 40 possible symbols that can be used in each of the 7 places
    number of such cases = 40^7 , assuming that repetition is allowed.
    But it also includes the case of 7 spaces, which technically would be a blank plate. I don't think they would allow that
    number of way = 40^7 - 1

    Your answer is correct as 1.64 x 10^11
    (subtracting my 1 has no effect on such a huge number)

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