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5 and 4 letter codes

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5 and 4 letter codes

by alex.gellatly » Mon May 21, 2012 6:56 pm
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

Thanks in advanced
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by Anurag@Gurome » Mon May 21, 2012 7:08 pm
alex.gellatly 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

Thanks in advanced
Number of ways to choose 5 different letters out of given 10 letters when the order of chosen letters matters (as for example code word ABCDE is different from BCDEA) = 10P5 = 10!(10 - 5)! = 10 * 9 * 8 * 7 * 6 = 30,240
Number of ways to choose 4 different letters out of given 10 letters when the order of chosen letters matters = 10P4 = 10!/(10 - 4)! = 10 * 9 * 8 * 7 = 5,040

Therefore, required ratio = 30,240/5,040 = 6/1 o r 6 to 1

The correct answer is E.
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by sam2304 » Mon May 21, 2012 7:19 pm
Ratio of 5 letter code to 4 letter codes = 10C5/10C4

We have 10 options for first letter, 9 options for second letter and so on ...

5 letter code word = 10 * 9 * 8 * 7 * 6
4 letter code word = 10 * 9 * 8 * 7

Divide one by the other we get 6/1.

IMO E.
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