To determine how many different passwords can be formed with the structure of 2 letters followed by 2 digits, we can break it down into two parts: the letters and the digits.
Step 1: Calculate the combinations for the letters
We have 26 letters in the English alphabet. Since the password consists of 2 letters, and each letter can be any of the 26 letters, the number of combinations for the letters is:
Number of combinations for letters = 26 (choices for first letter) * 26 (choices for second letter) = 676.
Step 2: Calculate the combinations for the digits
We have 10 digits (0 through 9). For the digit part of the password, as with the letters, we also have 2 digits. Therefore, the number of combinations for the digits is:
Number of combinations for digits = 10 (choices for first digit) * 10 (choices for second digit) = 100.
Step 3: Combine the results
Now, to find the total number of different passwords, we can simply multiply the combinations for the letters by the combinations for the digits:
Total number of passwords = 676 (letter combinations) * 100 (digit combinations) = 67,600.
Conclusion
Therefore, the total number of different passwords that can be formed with the structure of 2 letters followed by 2 digits is 67,600.