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.

## Comments

Sort by:

TopNewestWe 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, 7 months ago

Log in to reply

– Rashmi B K · 3 years, 7 months ago

Thanks !Log in to reply

Z is not a symmetric letter ;) – Ton De Moree · 3 years, 7 months ago

Log in to reply

– Daniel Chiu · 3 years, 7 months ago

Maybe Y was intended?Log in to reply

Y. Sorry for the mistake ! – Rashmi B K · 3 years, 7 months agoLog in to reply

Log in to reply

– Daniel Chiu · 3 years, 7 months ago

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.Log in to reply

– Gabriel Merces · 3 years, 7 months ago

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