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License plates in a particular state are to consist of 3 digits followed by 3 uppercase letters.
​c) How many different license plates can there be in this state if the first and second digits must be even​, and repetition of letters and numbers is not​ permitted?
​d) How many different license plates can there be in this state if the first digit cannot be 7​, and repetition of letters and numbers is not​ permitted?

 Apr 12, 2020
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c)  There are 5 even digits (0, 2, 4, 6, 8)

      First digit       = 5 possibilities

      Second digit  = 4 possibilities

      Third digit      = 8 possibilities

      First letter      = 26 possibilities

      Second letter = 25 possibilities

      Third letter     = 24 possibilities

      Total number of possibilities = 5 x 4 x 8 x 26 x 25 x 24 = ...

 

d)  First digit        = 9 possibilities

     Second digit   = 9 possibilities

     Third digit       = 8 possibilities

      First letter      = 26 possibilities

      Second letter = 25 possibilities

      Third letter     = 24 possibilities

      Total number of possibilities = 9 x 9 x 8 x 26 x 25 x 24 = ...

 Apr 12, 2020

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