Question

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?

Answer 1

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 $676 \cdot 10 \cdot 9 \cdot 8 \cdot 7 = \boxed{4,\!990,\!720}$.