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

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Senior Manager
Joined: 02 Dec 2007
Posts: 463
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If a code word is defined to be a sequence of different [#permalink]  19 Sep 2008, 09:25
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
Intern
Joined: 02 Sep 2008
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Re: code word [#permalink]  19 Sep 2008, 09:28
I come up with E. It is 6 to 1.
SVP
Joined: 21 Jul 2006
Posts: 1551
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Kudos [?]: 313 [0], given: 1

Re: code word [#permalink]  19 Sep 2008, 18:17
Nihit wrote:
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

I got E as well:

5-letter code: 10*9*8*7*6
4-letter code: 10*9*8*7

Therefore, the ratio is: (10*9*8*7*6)/(10*9*8*7) = 6/1
Director
Joined: 23 May 2008
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Re: code word [#permalink]  19 Sep 2008, 23:12
why do we use permutation here and not combination?
Re: code word   [#permalink] 19 Sep 2008, 23:12
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