### Instruction: How many five-digit zip codes exist such that each of the first three digits is greater than 4?### Response: I need to count the number of ways to choose the first three digits, and then multiply by the number of ways to choose the last two digits.
For each of the first three digits, I have five options: 5, 6, 7, 8, or 9.
So, the number of ways to choose the first three digits is 5 x 5 x 5 = 125.
For each of the last two digits, I have ten options: 0, 1, 2, ..., 9.
So, the number of ways to choose the last two digits is 10 x 10 = 100.
Therefore, the total number of zip codes is 125 x 100 = 12,500.