If we think about the possibilities of the passwords from right to left (i.e. let's think about how many different digits we can choose as the eighth digit in the password first), by the requirements, we have 2 digits can be chosen as the eighth digit (i.e 8 or 9). Now let's move one space to the left, how many different digits we can choose as the seventh digit? The candidates are 7,8 or 9, but one of these three digits already been chosen as the eighth digit, so we have just 2 digits left to be chosen as the seventh digits. If we proceed this way all the back to the first digit, we found out the the total number of possible passwords is just .

Roy