MR - License Plates Lesson
License Plates Lesson
Adapted from Course materials (1.A Student Activity Sheet 3) for AMDM developed under the leadership of the Charles A. Dana Center, in collaboration with the Texas Association of Supervisors of Mathematics and with funding from Greater Texas Foundation.
In the early 1900s, the State of Georgia issued its first license plates to owners of motor vehicles. Over the years, the license plates designs have varied by color, font size, and serial format, or alphanumeric arrangement. More recently, the designs offer drivers an option to show support of colleges, professions, and charity organizations. The state has also issued different types of license plates for specific motor vehicles such as historic vehicles, passenger vehicles, and dealer-owned vehicles.
In the 80s and 90s, passenger vehicles were issued with three letters followed by a space and three numerical digits. The state omitted the letters Q, U, and V from the possible letter selection until the year 2000. The "XXX" series of plates were the first series format to allow the restricted letters.
The series format was reversed in 2001; three numerical digits followed by a space and three letters.
In May 2012, the newest Georgia 2013 passenger plate was introduced to replace all active plates existing 1998-present. It is the state's first flat plate with the county created directly on the license plate. The serial format is the letter P followed by two letters and four numerical digits. The space between the letters and digits has been omitted.
Principle Scenario
How could you determine how many license plate numbers Georgia was able to assign during the early 1980s and 1990s? Remember that during this time there were three letter slots, three number slots, and the letters Q, U, and V were not being used.
The number of different license plate numbers that could be created is determined by multiplication, once you figure out a few specifics about the scenario:
Now, multiply using the results: (this is called the Counting Principle)
letter x letter x letter x number x number x number
23 x 23 x 23 x 10 x 10 x 10 = 12,167,000
Practice Questions
Additional Practice
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