A license plate consists of 2 uppercase letters followed by 4 digits. If repetition of letters is allowed, and repetition of digits is not allowed, how many different license plates are possible?
There are 26 choices for each of the two letters, making a total of $26 \cdot 26 = 676$ possibilities for the letters. There are 10 choices for the first digit, but only 9 remaining choices for the second digit, since repetition is not allowed. Continuing in this way, there are $10 \cdot 9 \cdot 8 \cdot 7$ possibilities for the digits. The desired total is the product of these two numbers, which is $676 \cdot 10 \cdot 9 \cdot 8 \cdot 7 = \boxed{4,\!990,\!720}$.
To calculate the number of different license plates possible, we need to consider the number of options for each position on the plate.
First, let's consider the two uppercase letters. Since repetition of letters is allowed, there are 26 possibilities for each letter.
Next, we have four digits. Since repetition of digits is not allowed, there are 10 possibilities for the first digit, 9 possibilities for the second digit, 8 possibilities for the third digit, and 7 possibilities for the fourth digit.
To find the total number of different license plates possible, we can multiply the number of possibilities for each position:
Number of possibilities for letters = 26 * 26 = 676
Number of possibilities for digits = 10 * 9 * 8 * 7 = 5,040
Total number of different license plates possible = 676 * 5,040 = 3,408,640
Therefore, there are 3,408,640 different license plates possible.