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Combinatorics, kaplan, 700 level, PS - unique 2 latter code

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Combinatorics, kaplan, 700 level, PS - unique 2 latter code [#permalink] New post 16 Oct 2011, 11:03
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42% (01:24) correct 57% (00:36) wrong based on 0 sessions
Each runner during a race is labeled with a unique one-letter code or a unique two-letter code, where the two letters are different. The codes use the 26-letter English alphabet, and if a given two letter code is used then the reverse code is not used. What is the maximum number of runners that can receive unique codes for the race?

A 325
B 351
C 677
D 650
E 676

guys please explain your answer I will provide OA after discussion
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-------Analyze why option A in SC wrong-------


Last edited by 144144 on 17 Oct 2011, 01:39, edited 1 time in total.
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Re: Combinatorics, kaplan, 700 level, PS - unique 2 latter code [#permalink] New post 19 Oct 2011, 11:53
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nishtil wrote:
Each runner during a race is labeled with a unique one-letter code or a unique two-letter code, where the two letters are different. The codes use the 26-letter English alphabet, and if a given two letter code is used then the reverse code is not used. What is the maximum number of runners that can receive unique codes for the race?

A 325
B 351
C 677
D 650
E 676

guys please explain your answer I will provide OA after discussion


1. 26 one letter code can be given(equal to number of alphabets)
2. Two letter codes

Number of possible 2 letter codes is equal to the sum of all the numbers between 25 and 1 (sum first 25 digits)

i.e, n(n+1)/2 = 325

Maximum number of runners that can receive unique codes = 325+26 =351
Ans B
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Re: Combinatorics, kaplan, 700 level, PS - unique 2 latter code   [#permalink] 19 Oct 2011, 11:53
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Moved topic 2 Combinatorics, kaplan, 700 level, PS - unique 2 latter code nishtil 1 16 Oct 2011, 11:03
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