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## Homework Statement

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?

## Homework Equations

## 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.