Question

On February 20, 2004, the Ohio Bureau of Motor Vehicles unveiled the state’s new license plate format. The plate consists of three letters (A–Z) followed by 4 digits (0–9). Assume that all letters and digits may be used, except that the third letter cannot be O, I, or Z. If repetitions are allowed, how many different plates are possible?

A) 26×26×23×10×10×10×10
B) 26×26×24×10×10×10×10
C) 25×25×24×10×10×10×10
D) 26×25×24×10×10×10×10

Answer 1

The total number of different license plates possible is found by multiplying the number of options for each segment of the plate. Since the first two letters have 26 options, the third letter has 23 (excluding O, I, Z), and each digit has 10 options, the calculation is 26 × 26 × 23 × 10 × 10 × 10 × 10. Therefore the correct answer is Option A.

Step-by-step explanation:

To find the number of different license plates possible, we need to multiply the number of options for each component of the license plate format. Since the plate consists of three letters followed by four digits, we have:

Number of options for the first letter: 26 letters (A-Z)

Number of options for the second letter: 26 letters (A-Z)

Number of options for the third letter: 23 letters (excluding O, I, and Z)

Number of options for the first digit: 10 digits (0-9)

Number of options for the second digit: 10 digits (0-9)

Number of options for the third digit: 10 digits (0-9)

Number of options for the fourth digit: 10 digits (0-9)

To calculate the total number of different plates possible, we multiply all these numbers together: 26 × 26 × 23 × 10 × 10 × 10 × 10. Simplifying, we get:

Total number of different plates possible: 26 × 26 × 23 × 10 × 10 × 10 × 10