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romitvsingh: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Fri Aug 19, 2011 12:13 amFollowed by: 1 member; Location: Delhi, India

by romitvsingh » Thu Nov 24, 2011 12:35 am

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?

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Source: Beat The GMAT — Problem Solving | Thu Nov 24, 2011 12:35 am

shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Thu Nov 24, 2011 1:00 am

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

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Thu Nov 24, 2011 3:55 am

romitvsingh wrote: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.

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