perm & comb..

[romitvsingh]

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?

[shankar.ashwin]

P(Using atleast 1) = 1 - P(Using None)

Since 26 alphabets are there (11 symmetrical and 15 asymmetric)

We have P(Using None) = 15/26 * 14/25 * 13/24 = 7/40

1- 7/40 = (40-7)/40 = 33/40

Ah! I read the question and it asks for number of such passwords,

So total possibilities = (26*25*24) out of which 33/40 of them will have at least one symmetric character.

So, 33/40 * (26*25*24) = 12870

[Anurag@Gurome]

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?

Possible 3 letter words = 26P3 = 26 * 25 * 24 = 15600
Since 11 are symmetric letters, so remaining 15 are asymmetric letters.
Possible 3 letter words with asymmetric letters = 15P3 = 2730
Possible words with at least one symmetric letter = 15600 - 2730 = 12870

The correct answer is 12870.