Questions: User passwords for a certain computer network consist of 2 letters followed by 2 numbers. How many different passwords are possible? Repetition is allowed.

Solution Steps

To determine the number of different passwords possible, we need to calculate the total number of combinations of letters and numbers. Since repetition is allowed, each letter and number can be chosen independently. There are 26 possible letters (A-Z) and 10 possible numbers (0-9). Therefore, the total number of passwords is the product of the number of choices for each character in the password.

For the password, we have 2 letters. Each letter can be any of the 26 letters in the English alphabet. Therefore, the total number of combinations for the letters is given by: \[ 26^2 = 676 \]

Next, we have 2 numbers in the password. Each number can be any of the 10 digits (0-9). Thus, the total number of combinations for the numbers is: \[ 10^2 = 100 \]

To find the total number of different passwords, we multiply the number of combinations for letters by the number of combinations for numbers: \[ \text{Total Passwords} = 676 \times 100 = 67600 \]

Final Answer