To determine the number of possible 5-digit zip codes when digits can be repeated, we start by noting that each digit in the zip code can be any digit from 0 to 9. This gives us a total of 10 possible choices for each digit.
A zip code consists of 5 digits, so we can calculate the total number of combinations as follows:
- For the first digit, there are 10 options (0-9).
- For the second digit, there are also 10 options.
- This pattern continues for the third, fourth, and fifth digits.
Therefore, the total number of 5-digit zip codes can be calculated using the formula:
Total Combinations = Number of Choices per Digit ^ Number of Digits
This means:
Total Combinations = 10 ^ 5
Calculating that gives:
10 ^ 5 = 100,000
So, there are 100,000 different 5-digit zip codes possible when digits can be repeated.