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
6 years, 1 month ago

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2 votes

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We can use complementary counting.

There are 26252426\cdot 25\cdot 24 passwords total.

There are 15141315\cdot 14\cdot 13 passwords without any letters symmetric.

Therefore, there are 262524151413=1287026\cdot 25\cdot 24-15\cdot 14\cdot 13=12870 passwords with at least one symmetric letter.

Daniel Chiu - 6 years, 1 month ago

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Thanks !

Rashmi B K - 6 years, 1 month ago

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Z is not a symmetric letter ;)

Ton de Moree - 6 years, 1 month ago

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Maybe Y was intended?

Daniel Chiu - 6 years, 1 month ago

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Ya ! It is Y. Sorry for the mistake !

Rashmi B K - 6 years, 1 month ago

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