Final answer:
Colorado ZIP Codes begin with 8 and have five-digit combinations with the second digit ranging from 0 to 4 and no restrictions on the last three digits. This results in 5,000 possible ZIP Code combinations (1 * 5 * 10 * 10 * 10). None of the provided options A to D is correct.
Step-by-step explanation:
The question addresses a combinatorics problem in the field of mathematics. Specifically, it asks about the number of possible five-digit ZIP Code combinations in Colorado, given certain restrictions. Since ZIP Codes in Colorado begin with the number 8 and the second digit can either be from 0 to 4, the number of possibilities for the second digit is 5 (0, 1, 2, 3, or 4). There are no restrictions on the remaining three digits, and since each digit can range from 0 to 9, there are 10 possibilities for each of these digits.
To calculate the total number of possible ZIP Code combinations, we multiply the number of options for each digit. This gives us:
- First digit: 1 possibility (the digit 8)
- Second digit: 5 possibilities (0 to 4)
- Third digit: 10 possibilities (0 to 9)
- Fourth digit: 10 possibilities (0 to 9)
- Fifth digit: 10 possibilities (0 to 9)
By multiplying the possible options for each position together, we get:
1 * 5 * 10 * 10 * 10 = 5,000 possible combinations
So, none of the provided options (A. 5 combinations, B. 10 combinations, C. 15 combinations, D. 20 combinations) are correct. The correct answer is 5,000 combinations.