# Discrete Math

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The licensing department issues plates with three letters followed by three digits for cars, and two letters followed by four digits for trucks, except that there are 137 "objectionable" three-letter prefixes that cannot be used. How many vehicles can be licensed?

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Number of plates for cars with three letters followed by three digits = 26*26*26*10*10*10 = 17,576,000

Number of plates for trucks with two letters followed by four digits = 26*26*10*10*10*10 = 6,760,000

There are 137 "objectionable" three-letter prefixes that cannot be used.

Number of license plates that cannot be used = 137*10*10*10 = 137000

Number of vehicles that can be licensed = (17,576,000+6,760,000) - 137000 = 24,199,000

Answer: 24,199,000 vehicles

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