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# If a code word is defined to be a sequence of different

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Intern
Joined: 08 Nov 2008
Posts: 38
If a code word is defined to be a sequence of different [#permalink]

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11 Nov 2008, 14:07
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?

A. 5 to 4
B. 3 to 2
C. 2 to 1
D. 5 to 1
E. 6 to 1

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VP
Joined: 17 Jun 2008
Posts: 1479

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12 Nov 2008, 00:15
stallone wrote:
e ; 10P5/10P6

It will be 10P5 / 10P4
Manager
Joined: 14 Oct 2008
Posts: 158

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12 Nov 2008, 00:39
Why not 10C5 / 10C4 ? I did'nt understand how is it not combinations problem ? Number of 5 letter words can be chosen from 10 letters in 10C5 ways ??? Although I am getting the ratio to be 6/5 if use Combinations, hence it has o be incorrect. Can anyone explain pls.
CEO
Joined: 17 Nov 2007
Posts: 3486
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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12 Nov 2008, 00:57
gameCode wrote:
Why not 10C5 / 10C4 ? I did'nt understand how is it not combinations problem ? Number of 5 letter words can be chosen from 10 letters in 10C5 ways ??? Although I am getting the ratio to be 6/5 if use Combinations, hence it has o be incorrect. Can anyone explain pls.

ABCDE and ABCED is different codes as the problem says: "a sequence of different letters"

Faster solution: We can create 5-letters code from 4-letters code by adding one letter of 10-4=6 letters. So, 6 to 1.

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Re: letter code--27   [#permalink] 12 Nov 2008, 00:57
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# If a code word is defined to be a sequence of different

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