Question

fundamental counting principle

a license plate consists of 2 letters (a-z) followed by 3 digits (0-9). if letters and digits can be repeated, how many license plates can be created?

number of plates = ?

Explanation:

Identify the choices for each position

The license plate consists of 5 positions: 2 letters followed by 3 digits.

• For each letter position, there are 26 possible choices (A-Z).
• For each digit position, there are 10 possible choices (0-9).

Apply the Fundamental Counting Principle

Since repetition is allowed, the choices for each position are independent.
We multiply the number of possibilities for each of the 5 positions:

$$ \text{Total Plates} = 26 \times 26 \times 10 \times 10 \times 10 $$

Calculate the final product

We compute the multiplication:

$$ 26^2 = 676 $$

$$ 10^3 = 1000 $$

$$ 676 \times 1000 = 676,000 $$

Answer:

A license plate consists of 2 letters (A-Z) followed by 3 digits (0-9). If letters and digits can be repeated, how many license plates can be created?

Number of Plates = <blank>676,000</blank>