pre calculus

There are a total of 676 possible license plates with two letters followed by four digits of which the first digit is not zero. When creating license plates, the first two positions can be filled with any of the 24 available letters (excluding I, 0, and Q). This means there are 24 x 24, or 576 possible combinations of two letters. Then, each of those 576 combinations can be combined with any of the nine available digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) in the four remaining positions. That is 576 x 9, or 5,184 possible combinations for the four digits. However, since the first digit of the four digits cannot be zero, there are only 8 (instead of the 9 total) possible digits for the first position. Multiplying the 576 existing two-letter combinations with the 8 available digits results in a total of 5,76 x 8, or 4,608 possible combinations. Therefore, there are a total of 676 different possible license plates with two letters followed by four digits of which the first digit is not zero.