1. The problem statement, all variables and given/known data How many eight-letter passwords using the letters A-Z are there in which up to one letter is allowed to be used more than once? 2. Relevant equations 3. The attempt at a solution I broke the problem up based on repetition of one letter: (26)8 ways with no repetition, (8 choose 2)*26*(25)6 ways with letter repeated once, (8 choose 3)*26*(25)5 ways with letter repeated twice, and so on, until 26 ways with letter repeated 7 times filling all 8 spaces. Adding these 8, gives the total ways.