Question

A computer randomly generates a 4-character password of 2 letters followed by 2 digits. All passwords Are equally likely.What is the number of possible 2-letter, 2-digit passwords?

Answer 1

The total number of possible 2-letter, 2-digit passwords is calculated by multiplying the number of letter choices (26 times 26) by the number of digit choices (10 times 10), resulting in 67,600 different passwords.

Step-by-step explanation:

To calculate the number of possible 2-letter, 2-digit passwords, we consider the number of choices for each character independently. For the letters, there are 26 options for the first letter and 26 options for the second letter since the English alphabet contains 26 letters. For the digits, there are 10 options for the first digit (0 through 9) and 10 options for the second digit.

The total number of possible passwords is then the product of these individual choices:

• Number of letter choices: 26 × 26 = 676
• Number of digit choices: 10 × 10 = 100

To find the total number of combinations, we multiply the number of letter choices by the number of digit choices:

Total number of combinations = 676 × 100 = 67,600 possible passwords.