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Try to Permute

Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter?

I tried and ended up with no answer.

Note by Rashmi B K
3 years, 5 months ago

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We can use complementary counting.

There are \(26\cdot 25\cdot 24\) passwords total.

There are \(15\cdot 14\cdot 13\) passwords without any letters symmetric.

Therefore, there are \(26\cdot 25\cdot 24-15\cdot 14\cdot 13=12870\) passwords with at least one symmetric letter. Daniel Chiu · 3 years, 5 months ago

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@Daniel Chiu Thanks ! Rashmi B K · 3 years, 5 months ago

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Z is not a symmetric letter ;) Ton De Moree · 3 years, 5 months ago

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@Ton De Moree Maybe Y was intended? Daniel Chiu · 3 years, 5 months ago

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@Daniel Chiu Ya ! It is Y. Sorry for the mistake ! Rashmi B K · 3 years, 5 months ago

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Comment deleted Oct 15, 2013

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@Gabriel Merces This is wrong because there can be more than one symmetric letter, and also if there is one letter it can be the 1st or 2nd letter in the password. Daniel Chiu · 3 years, 5 months ago

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@Daniel Chiu I Agree , You are Correct ! Excuse-me For Error !! Thank Very Much Daniel ! Gabriel Merces · 3 years, 5 months ago

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