To determine how many different passwords can be formed with the structure of 2 letters followed by 2 digits, we need to break down the components.
First, consider the letters. The English alphabet has 26 letters. If we are creating a password with 2 letters:
- The first letter can be any of the 26 letters.
- The second letter can also be any of the 26 letters.
So, the total combinations for the letters would be:
26 (first letter) × 26 (second letter) = 676 combinations.
Next, look at the digits. There are 10 possible digits (0 through 9). For the 2 digits in the password:
- The first digit can be any of the 10 digits.
- The second digit can also be any of the 10 digits.
So, the total combinations for the digits would be:
10 (first digit) × 10 (second digit) = 100 combinations.
Finally, to find the total number of different passwords that can be formed, multiply the combinations of letters and digits:
676 (letter combinations) × 100 (digit combinations) = 67,600 different passwords.
In conclusion, with 2 letters followed by 2 digits, you can create a total of 67,600 different unique passwords.