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Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same

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Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same [#permalink]

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New post 21 Aug 2016, 23:51
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Question Stats:

61% (01:54) correct 39% (02:20) wrong based on 98 sessions

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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?

A. 2,145
B. 6,435
C. 12,100
D. 12,870
E. 25,740
[Reveal] Spoiler: OA

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Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same [#permalink]

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New post 22 Aug 2016, 05:34
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Bunuel 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?

A. 2,145
B. 6,435
C. 12,100
D. 12,870
E. 25,740



Since we are given atleast one symmetric letter in the three letter word we can take the following cases

1. All three
2. One symmetry and other two non
3. Two symmetry and one non
4. All the three letters can be arranged in 6 ways

( 11c3 + 11c1 * 15c2 + 11c2 * 15c1 ) * 6

( 11*10*9/ 6 + 11 * 15 * 14 / 2 + 11*10 / 2 * 15 ) * 6

12870

IMO option D is the correct answer..

OA please...will correct if I missed anything..
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Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same [#permalink]

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New post 22 Aug 2016, 07:09
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Total 3 letter passwords = 26 * 25 * 24 = 15600

Total letters = 26 = symmetrical letters (11) + asymmetrical letters (x) => x = 15

Total no. of 3 letters passwords using asymmetrical letters = 15 * 14 * 13 = 2730 (no repetition allowed)

Hence, no. of 3 letter passwords using atleast one symmetrical letter = 15600 - 2730 = 12870 ---> Option D
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Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same [#permalink]

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New post 23 Apr 2017, 14:09
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udyans123 wrote:
Total 3 letter passwords = 26 * 25 * 24 = 15600

Total letters = 26 = symmetrical letters (11) + asymmetrical letters (x) => x = 15

Total no. of 3 letters passwords using asymmetrical letters = 15 * 14 * 13 = 2730 (no repetition allowed)

Hence, no. of 3 letter passwords using atleast one symmetrical letter = 15600 - 2730 = 12870 ---> Option D


I am still confusing between kCn and kPn, I thought kPn should be applied to this question, can you explain the concepts for me?
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Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same [#permalink]

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New post 07 May 2017, 21:58
A quick observation about the question.
Z is not a symmetric letter by this definition.
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Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same [#permalink]

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New post 27 Aug 2017, 19:58
this tests the ability to calculate fast and accurate
Re: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same   [#permalink] 27 Aug 2017, 19:58
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Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same

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