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.

Easy Math Editor

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Comments

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 - 7 years, 8 months ago

Thanks !

Rashmi B K - 7 years, 8 months ago

Z is not a symmetric letter ;)

Ton de Moree - 7 years, 8 months ago

Maybe Y was intended?

Daniel Chiu - 7 years, 8 months ago

Ya ! It is Y. Sorry for the mistake !

Rashmi B K - 7 years, 8 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$