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

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SVP
Joined: 21 Jul 2006
Posts: 1510
If a code word is defined to be a sequence of different [#permalink]

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14 Apr 2008, 13:09
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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

Would someone please show me how to solve this problem?
thanks
Director
Joined: 10 Sep 2007
Posts: 938

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14 Apr 2008, 13:28
Possibilities for 5 letter word = 10*9*8*7*6 (First letter can any one of 10, next can anyone of remaining 9, and so on)
Possibilities for 4 letter word = 10*9*8*7

Ratio = 10*9*8*7*6/10*9*8*7 = 6/1

Senior Manager
Joined: 29 Jan 2007
Posts: 441
Location: Earth

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14 Apr 2008, 17:27
That was cool Abhijit.

I got the answer different way that is more convoluted in a way

I did it like this

$$Number of ways = (5! * 10C5)/(4! * 10C4)$$
SVP
Joined: 28 Dec 2005
Posts: 1557

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14 Apr 2008, 17:30
do we assume no repitition here ?
Director
Joined: 10 Sep 2007
Posts: 938

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14 Apr 2008, 18:07
pmenon wrote:
do we assume no repitition here ?

Repetition is always mentioned in the question, by default assume all questions to be non-repetition cases.
Re: PS: Ratios   [#permalink] 14 Apr 2008, 18:07
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