1. The problem statement, all variables and given/known data To gain access to his account, a customer using an automatic teller machine (ATM) must enter a four digit code. If repetition of the same four digit is not allowed (for example, 1111), how many possible combinations are there? 3. The attempt at a solution I figured two possible solutions. I do not know which one is correct and why the other one is not. Possibility 1: Considering 3 digits which can have 10 combinations each (0-9) and the last digit which can only have 9 combinations, to prevent the repetitions of all 4 digits; we have 10 X 10 X 10 X 9 = 9000 Possibility 2: Considering that the number of combinations that are not allowed are 10 (0000, 1111, 2222, ..., 9999), we just take the total no. of possible combinations and subtract 10 from it. Thus, (10^4) - 10 = 9990 I am biased towards the 2nd possibility but do not understand why the first one is wrong. Explanation/help would be very much appreciated.