Forming License Plates A license plate is designed so that the first two characters are letters and the last four characters are digits (0 through 9). How many different license plates can be formed assuming that letters and numbers can be used more than once?

Verified step by step guidance

1. Identify the total number of characters in the license plate: 2 letters followed by 4 digits, making a total of 6 characters.
2. Determine the number of possible choices for each letter. Since letters can be repeated and there are 26 letters in the English alphabet, each letter position has 26 possibilities.
3. Determine the number of possible choices for each digit. Since digits can be repeated and there are 10 digits (0 through 9), each digit position has 10 possibilities.
4. Calculate the total number of different license plates by multiplying the number of possibilities for each position: \$26 \times 26 \times 10 \times 10 \times 10 \times 10$.
5. Express the final answer as the product of these values, representing the total number of unique license plates possible under the given conditions.

Key Concepts

Counting Principle

The counting principle states that if there are multiple independent choices to be made, the total number of outcomes is the product of the number of options for each choice. In this problem, the total number of license plates is found by multiplying the number of choices for letters and digits.

Permutations with Repetition

Permutations with repetition allow elements to be repeated in each position. Since letters and digits can be used more than once, each position can be chosen independently from the full set of possible characters, increasing the total number of combinations.

Character Sets for License Plates

The license plate format specifies two letters followed by four digits. Letters come from the 26-letter English alphabet, and digits range from 0 to 9, giving 10 possible digits. Understanding these sets is essential to calculate the total number of possible plates.