License Plates and Permutations
Topic
License Plates and Permutations
Vocabulary
 Permutations
 Permutations with Repetition
 Combinations
Student Exploration
How many license plates are possible in the U.K.?
License plates, also known as vehicle registration plates, are used for authorizes to be able to track vehicles and determine who the owner of a vehicle is. Whenever you purchase a car you have to register it and order plates for your vehicle. And then, whenever the police need to give a person a parking or speeding ticket, they use the plates number to enter the ticket into the police system.
In the United Kingdom (U.K.) the license plates are made up of the regional flag followed by a twodigit local area code, a twodigit age identifier (corresponding to the year the vehicle is registered), followed by a threedigit sequence of letters. See the image below for a visual, from http://en.wikipedia.org/wiki/Vehicle_registration_plates_of_the_United_Kingdom#Current_system .
 1. Given the constraints stated above, how many different license plates are possible in the U.K.?
Extension Investigation
 2. Why is this a Permutation problem, rather than a Combination problem? Explain.
 3. Why is this a Permutation with Repetitions problem? Explain.
 4. Need a little help? Here are some steps to help you.

 a. Let’s say that the year is set. Calculate how many of the random threeletter sequences are possible at the end of the license plate.

 b. Next, calculate how many twodigit year identifiers are possible.

 c. Next, calculate how many twoletter area codes are possible.

 d. Now, calculate how many of the twoletter area codes, followed by twodigit year identifiers, followed by the random threeletter sequences are possible.
 5. How would you approach this problem differently if letters and digits could not be repeated? Explain.
 6. Research what the license plates (or vehicle registration plates) requirements are in your state or country. Then calculate how many different plates are possible in your state or country based on the license plate set up.
Resources Cited
http://en.wikipedia.org/wiki/Vehicle_registration_plates_of_the_United_Kingdom#Current_system
Connections to other CK12 Subject Areas
 Probability and Permutations
 Permutations and Combinations Compared
 Permutation Problems
 Combinations.
Image from:
http://en.wikipedia.org/wiki/Vehicle_registration_plates_of_the_United_Kingdom#Current_system