Final answer:
Using permutation principles, there are 100,000 different possible 5-digit passwords for the school email system, assuming each digit can range from 0 to 9 and repetitions are allowed.
Step-by-step explanation:
To calculate how many 5-digit numerical passwords are possible for the school email system, you would use the principles of permutations. Since the question seems incomplete, we’ll assume that each digit can be anything from 0 to 9 and that digits can be repeated.
The number of options for the first digit is 10 because it can be any digit from 0-9. The same applies to the second, third, fourth, and fifth digits. Thus, you multiply the number of options for each place value.
The calculation is as follows:
10 options for the 1st digit × 10 options for the 2nd digit × 10 options for the 3rd digit × 10 options for the 4th digit × 10 options for the 5th digit = 100,000 different possible 5-digit passwords.