Correct Customer account "numbers" for a certain company consist of 3 letters followed by 2 numbers. Step 2 of \( \mathbf{2} \) : How many different account numbers are possible if repetitions of letters and digits are not allowed?

To calculate the total number of different customer account numbers possible without repetitions, let's break it down. 1. For the three letters: There are 26 letters in the English alphabet. - For the first letter, you have 26 options. - For the second letter (since repetitions are not allowed), you have 25 options remaining. - For the third letter, you have 24 options left. Therefore, the total combinations for letters is: \[ 26 \times 25 \times 24 \] 2. For the two digits: There are 10 digits (0-9). - For the first digit, you have 10 options. - For the second digit, you have 9 options remaining. So, the total combinations for digits is: \[ 10 \times 9 \] Now, to find the total number of different account numbers, multiply the combinations of letters by the combinations of digits: \[ (26 \times 25 \times 24) \times (10 \times 9) = 15600 \times 90 = 1404000 \] Thus, there are 1,404,000 different possible customer account numbers.