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by dunkin77 » Thu Jun 28, 2007 3:42 am
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


Hi, I dont understand the meaning of the question....Can anyone help explain?
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by mschling52 » Thu Jun 28, 2007 4:54 am
Is it E? We want to find how many unique code words there are of length 5 and of length 4. Since order matters (i.e. ABCD is a different code word than DCBA) we can use the formula for permutations

nPr = n!/((n-r)!)

which will give us the number of different ways to pick r objects from a set of n objects. So, the ratio we are interested in is

(10 P 5)/(10 P 4) = (10!/5!)/(10!/6!) = 6!/5! = 6,

giving us a ratio of 6-to-1.
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by f2001290 » Thu Jun 28, 2007 6:06 am
One more for 6:1

No. of 5 letter codes = 10*9*8*7*6

No. of 4 letter codes = 10*9*8*7
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