Answer: 676 million different possible reservation numbers following this format.
Step-by-step explanation: To determine the total number of possible reservation numbers, you can multiply the number of choices for each part of the reservation number.
1. **3 digits:** There are 10 possible digits (0-9) for each of the three positions. So, \(10 \times 10 \times 10 = 1000\) possibilities for the three digits.
2. **2 letters:** There are 26 letters in the English alphabet. Since the letters can be repeated, there are \(26 \times 26 = 676\) possibilities for the two letters.
3. **3 digits:** Similar to the first part, there are \(10 \times 10 \times 10 = 1000\) possibilities for the three digits.
Now, multiply the possibilities for each part to find the total number of reservation numbers:
\[1000 \times 676 \times 1000 = 676,000,000.\]
Therefore, there are 676 million different possible reservation numbers following this format.