Final answer:
To calculate the number of possible license plates with given restrictions, we calculated permutations for digits and letters separately. The digits contribute 1,000 combinations, while the letters contribute 12,167 combinations. Multiplying these gives us 12,167,000 possible license plates.
Step-by-step explanation:
The question relates to permutations and combinations in mathematics, specifically in the context of license plate configurations. We need to calculate the total number of different license plates possible given the restrictions stated for a 2014 New Jersey license plate.
Firstly, for the three digits (0-9), since each position can have 10 different digits, the number of combinations for the digits is 10 × 10 × 10, which equals 1,000.
Next, for the three letters, typically, each position could have 26 possibilities if we consider all letters A-Z. However, we have restrictions: The fourth position cannot have letters D, T, or X, and no position can have the letters I, O, or Q.
This leaves us 23 possible letters for the fourth position and 23 for the fifth and sixth as well, since the exclusions are consistent across the alphabet. So, the number of combinations for the letters is 23 × 23 × 23, which equals 12,167.
Finally, to find the total number of different license plates, we multiply the two results: 1,000 × 12,167 = 12,167,000 possible license plates.