To determine how many possible 9-digit zip codes can be created if the first digit cannot be zero, we need to break down the problem based on the constraints given.
The first digit of the zip code can be any digit from 1 to 9 (since it cannot be zero). This gives us 9 possible choices for the first digit.
For the remaining 8 digits, each digit can be any digit from 0 to 9, providing us with 10 possible choices for each of those positions.
So, the total number of possible zip codes can be calculated as follows:
- Choices for the first digit: 9
- Choices for each of the other 8 digits: 10
The total number of combinations can be calculated with the formula:
Total Combinations = (Choices for First Digit) x (Choices for Second Digit) x ... x (Choices for Ninth Digit)
In this case:
Total Combinations = 9 x 10^8
Calculating this gives us:
Total Combinations = 9 x 100000000 = 900000000
Therefore, if the first digit cannot be zero, there are 900 million possible 9-digit zip codes.