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5-letter code vs 4-letter code

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by crackgmat007 » Wed May 13, 2009 9:01 pm
5. 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

Answer seems to be 6to1
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by bluementor » Wed May 13, 2009 11:50 pm
In a 5-letter code, the first letter could take any of the 10 letters. The 2nd letter could take any of the remaining 9 letters (since 1 letter has been choosen for the first letter). The third letter could take any of the 8 letters and so on....

So, the number of different 5-letter code words = 10x9x8x7x6

and similarly,

the number of different 4-letter code words = 10x9x8x7

Ratio = (10x9x8x7x6)/(10x9x8x7) = 6

Ratio = 6:1

Choose E.

-BM-
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by sureshbala » Thu May 14, 2009 3:35 am
Total number of 5 letter codes = 10P5

Total number of 4 letter codes = 10P4

Ratio = 10P5:10P4 = 6:1
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