Question

Some states are running out of license plate numbers. Delaware currently uses six-digit numbers in its license plate numbering system. The state of Washington recently stated that it needs to explore options to replace their current system of three numerical digits followed by three letters. New Jersey currently uses a system of one letter, two numerical digits, then three letters. How could the state of Washington change their license plate system to address the possible problem of running out of plate numbers? a. Washington can use 6 digits or letters for their numbering system. b. Washington can use more than 6 digits or letters for their numbering system. c. Washington can use 3 digits or 3 letters for their numbering system. d. Washington can use 6 letters for their numbering system.

Answer 1

The answer is letter d

Explanation:

This problem is a basic combinatory statistical problem:

Right now Washington uses 3 numerical digits (ranging from 0 to 9 each) and three letters (ranging from A to Z). So each number can be one in 10 and each letter can be one in 26 (the amount of numbers that the alphabet has).

Given n= the amount of possible licence plates and a= the amount of numbers ranging from 0 to 9 (10 possibilities) and b= the amount of letters ranging from A to Z (26 possibilities)

n=a*a*a*b*b*b=17.576.000

So if we switch one a to a b, we increment the amount of possible outputs, that is why when switching all the numbers to letters we exponentially increase the amount of possible license plantes.