(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Combinatorics Question: 8-Letter Passwords

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