How many password combination?

Question

How many password combinations if you can have up to 8 letters, uppercase or lowercase, with only letters and no numbers or special characters?

My attempt: $$52+52^2+52^3+52^4+52^5+52^6+52^7+52^8$$ because there are 52 possible at each place and you can have up to 8 letters which means you can have either 1 2 3 4 5 6 7 or 8 letters. Is this correct? My reasoning could be off. Thank you!

Seems correct. There could be one more for the empty password. — user2345215, Nov 15 '14 at 09:31
Well since they ask for a password, I assumed they mean you have to have at least 1 letter. But thank you for answering! — bodygued, Nov 15 '14 at 09:34
My experience with Windows 2000 showed that asking for a password doesn't mean asking for a non-empty password. — Asaf Karagila, Nov 15 '14 at 09:35

score 0 · Answer 1 · answered Nov 15 '14 at 10:48

0

Assuming non-empty passwords your answer is fine. Note that you can compute this as $$\frac{1 - 52^9}{1 - 52} = 54.507.958.502.661$$ if you allow the empty password, and that $-1$ if not.

answered Nov 15 '14 at 10:48

Henno Brandsma

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How many password combination?

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