Final answer:
Using permutation principles, a state issuing license plates with two letters followed by four digits can issue 676,000 different plates, calculated as 26 possibilities for each letter and 10 for each digit.
Step-by-step explanation:
If a state issued license plates using the scheme of two letters followed by four digits, the number of different license plates that can be issued can be calculated based on the principle of counting, also known as permutation and combination in mathematics. Each of the two letters can be one of 26 possibilities (assuming no distinction between uppercase and lowercase), and each of the four digits can be one of 10 possibilities (0 through 9).
To find the total number of combinations, we multiply the number of possibilities for each position:
- For the first letter, there are 26 possibilities.
- For the second letter, there are 26 possibilities.
- For the first digit, there are 10 possibilities.
- For the second digit, there are 10 possibilities.
- For the third digit, there are 10 possibilities.
- For the fourth digit, there are 10 possibilities.
Therefore, the total number of different license plates possible is:
26 (first letter) × 26 (second letter) × 10 (first digit) × 10 (second digit) × 10 (third digit) × 10 (fourth digit) = 676,000.
Hence, a state can issue 676,000 different license plates with this scheme.