License plates in a certain province consist of three letters followed by three digits. How many di erent plates are possible if no repetitions of letters or digits are allowed?

Answer 1

This problem is listed as 'Elementary Math', so I will keep the answer very straight forward.

The license plate has 6 spaces available: 3 for letters and 3 for digits. There are 26 letters available in the alphabet (A-Z) and 10 digits available (0-9). They key to this problem is that repetition is not allowed for either the letters or the numbers.

(1) There are 26 possible letters that can be used in the first space. After one letter is used in the first space, since repetition is not allowed, there are 25 possible letters that can be used in the second space. Following the same logic, there are 24 possible letters that can be used in the third space.

The total number of possible combinations for the first three spaces in the license plate is 26 * 25 * 24 = 15,600.

The same logic as (1) can be applied to the last three digits in the license plate, and the final two numbers can be multiplied together to find the answer to the problem.

Hopefully this clarifies how to approach the problem and you can solve the rest on your own!