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
5 years 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 - 5 years ago

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Thanks !

Rashmi B K - 5 years ago

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Z is not a symmetric letter ;)

Ton de Moree - 5 years ago

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Maybe Y was intended?

Daniel Chiu - 5 years ago

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Ya ! It is Y. Sorry for the mistake !

Rashmi B K - 5 years ago

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Comment deleted Oct 15, 2013

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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 - 5 years ago

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I Agree , You are Correct ! Excuse-me For Error !! Thank Very Much Daniel !

Gabriel Merces - 5 years ago

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