Final answer:
There are 648 possible access codes for a computer system that requires a three-digit number that does not start with zero and does not repeat digits. The number of options for each digit is multiplied together (9 options for the first digit, 9 options for the second digit after considering zero, and 8 for the third digit), resulting in a total of 648 possible combinations.
Step-by-step explanation:
To determine the number of possible access codes for a computer system that requires a three-digit number where the first digit cannot be zero and there can be no repeating digits, we use the principle of counting known as permutations. Since the code is a three-digit number where no digit can be repeated and the first digit cannot be zero, we have the following possibilities:
- For the first digit, since it cannot be zero, there are 9 possible choices (1 through 9).
- For the second digit, we can choose any of the remaining 9 digits (0 can now be used, but we cannot reuse the first digit).
- For the third digit, we have 8 remaining choices (since we cannot use the first or second digit again).
Using the multiplication principle of counting, we multiply the number of choices for each position together:
9 (choices for the first digit) * 9 (choices for the second digit) * 8 (choices for the third digit) = 9 * 9 * 8 = 648
Therefore, there are 648 different possible access codes following these restrictions.