A password consists of 3 letters of the alphabet followed by 3 digits chosen from 0 to 9. Repetition is allowed. How many different possible passwords are there? Your Answer: Answer

To create a password consisting of 3 letters followed by 3 digits, we first calculate the number of options for each part. There are 26 letters in the alphabet, and for each of the 3 letters, we have 26 options. This gives us \(26^3\) combinations for the letters. For the digits, there are 10 options (0 to 9) for each of the 3 digits, resulting in \(10^3\) combinations for the digits. Therefore, the total number of different possible passwords is: \[ 26^3 \times 10^3 = 17576 \times 1000 = 17,576,000 \] So, there are a total of **17,576,000 different possible passwords**.