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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
4 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.

- 4 years ago

Thanks !

- 4 years ago

Z is not a symmetric letter ;)

- 4 years ago

Maybe Y was intended?

- 4 years ago

Ya ! It is Y. Sorry for the mistake !

- 4 years ago

Comment deleted Oct 15, 2013

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.

- 4 years ago

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

- 4 years ago