Final answer:
The number of different license plates possible in a state with the format of three digits followed by three uppercase letters, without repetition, is 247,104,000.
Step-by-step explanation:
The student's question relates to the combinations possible for vehicle license plates with a specific format: three digits followed by three uppercase letters, where repetition is not allowed. To calculate the number of different license plates, we need to consider the number of choices for each position and apply the basic principle of counting.
For the digits part (the first three positions), since repetition is not permitted, the first digit can be any of the 10 possible digits (0-9), the second digit can be any of the remaining 9 digits, and the third digit can be any of the remaining 8 digits. Thus, for the three digits, there are 10 × 9 × 8 possibilities.
For the letters part (the last three positions), we use the 26 letters of the English alphabet, again without repetition. So, the first letter has 26 options, the second letter has 25 remaining options, and the third letter has 24 options. Hence, for the three letters, there are 26 × 25 × 24 possibilities.
To find the total number of different license plates, we multiply the possibilities of the digits part with the possibilities of the letters part which gives us:
Total number of plates = (10 × 9 × 8) × (26 × 25 × 24) = 15,840 × 15,600 = 247,104,000
Therefore, there can be 247,104,000 different license plates in this state.