Final answer:
The number of possible license plates can be calculated using combinations of uppercase English letters and digits. For three digits and three letters, you calculate 2 times 10 to the power of 3 times 26 to the power of 3. For four letters and two digits or three letters and three digits, you calculate 26 to the power of 4 times 10 to the power of 2 plus 26 to the power of 3 times 10 to the power of 3.
Step-by-step explanation:
The question involves calculating the number of possible license plates that can be created under two different scenarios using combinations of uppercase English letters and digits.
For scenario A, a license plate can have either three digits followed by three uppercase English letters or vice versa. The number of possibilities for three digits is 103 (as there are 10 digits: 0-9) and for three uppercase letters is 263 (as there are 26 letters in the English alphabet). Therefore, the total number of license plates for either configuration is 2 × (103 × 263).
For scenario B, a license plate can have either four uppercase English letters followed by two digits or three uppercase English letters followed by three digits. The number of possible combinations for the first configuration is 264 × 102, and for the second configuration is 263 × 103. The total number of license plates for both configurations combined is (264 × 102) + (263 × 103).