Final answer:
To find the total number of possible license plates, multiply the number of options for each component of the plate. The formula is 10³ × 26⁴ × 10, where 10³ is for the three digits, 26⁴ is for the four letters, and another 10 for the final digit, leading to the correct answer, which is (c) 10³ × 26⁴ × 10.
Step-by-step explanation:
The question asks for the number of different license plates that can be formed with a specific format using 3 digits, 4 letters, and then 1 digit. Since each letter or digit can repeat, we use the multiplication principle to calculate the total number of possibilities. We have 10 options for each digit (0-9) and 26 options for each letter (A-Z). The license plate format can therefore be represented as DDDLLLLD, where 'D' stands for a digit and 'L' stands for a letter.
The total number of possible license plates can be calculated by taking the product of the number of options for each position, which gives us the formula:
10³ × 26⁴ × 10
To explain further, there are 10 choices for the first digit, 10 choices for the second digit, and 10 choices for the third digit, which is 10 × 10 × 10 = 10³ options for the digits. For the letters, there are 26 choices for the first letter, 26 for the second, 26 for the third, and 26 for the fourth letter, total of 26 × 26 × 26 × 26 = 26⁴ options. Lastly, there's one more digit at the end, which brings another 10 options. Multiplying these all together gives the total number of possible license plates.