1. The problem statement, all variables and given/known data Each user on a computer has a password, which is six to eight characters long, where each character is an uppercase letter or a digit. Each password must contain at least one digit . How many possible passwords are there? 2. Relevant equations 3. The attempt at a solution My reasoning was as follows: First, for passwords with length 6, we can choose the 6 places where at least one digit will go, and that digit can be chosen in 10 different ways. Then we multiply this by ##36^5##, since that is the number of choices we have for the other characters in the password of length 6. We apply similar reasoning to passwords of length 7 and length 8, and get ##10 \cdot 6 \cdot 36^5 + 10 \cdot 7 \cdot 36^6 + 10 \cdot 8 \cdot 36^7##. However, this is not the right answer. Where am I going wrong?