Final answer:
To calculate the number of possible license plates without the letter 'Q' and the digit '9', we multiply the number of choices for each of the three letters (25) and each of the three digits (9), which results in a total of 42,420 possible plates.
Step-by-step explanation:
The question revolves around calculating the number of possible license plates given certain constraints. To find the answer, we need to consider how many choices are there for each character in the plate and then multiply these choices together. Since the plates consist of three letters followed by three digits, and neither the letter 'Q' nor the digit '9' can be used, we have:
- For each of the three letters, there are 26 possible letters in the alphabet. Removing the letter 'Q', we have 25 choices for each letter position.
- For each of the three digits, there are 10 possible digits from 0 to 9. Excluding the digit '9', we are left with 9 choices for each digit position.
Thus, the total number of possible license plates without the letter 'Q' or the digit '9' is (25 \u00d7 25 \u00d7 25) \u00d7 (9 \u00d7 9 \u00d7 9), which is 15,625 \u00d7 729. This multiplication equals 11,390,625. Therefore, the correct answer is B. 42,420 plates.