Question

The latest automobile license plates issued by the California Department of Motor Vehicles begin with a single numeric digit, followed by three letters, followed by three more digits. How many different license "numbers" are available using this scheme?

Answer 1

Solution

The solution is derived under the following assumptions:

1. Number of numerical digits permitted is 10, namely, 0, 1, 2, …… , 9

2. Number of letters permitted is 26, namely, the 26 letters of English alphabet, either in capital case or in lower case, but not both.

3. The same digit and the same letter can appear any number of times in the same license plate, subject of course to other given restrictions, i.e., as an extreme example, 0AAA000 is a permissible license plate.

Now to work out the solution,

The first character can be any one of the 10 digits in 10 ways.

The second character can be any one of the 26 letters in 26 ways.

The third character can be any one of the 26 letters in 26 ways.

The fourth character can be any one of the 26 letters in 26 ways.

The fifth character can be any one of the 10 digits in 10 ways.

The sixth character can be any one of the 10 digits in 10 ways.

The seventh character can be any one of the 10 digits in 10 ways.

Thus, total number plates that can formed is: 10 x 26 x 26 x 26 x 10 x 10 x 10

= 175760000 Answer

DONE