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If a code word is defined to be a sequence of different letters chosen
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14 Apr 2022, 02:00
14 Apr 2022, 02:00
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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
A. 5 to 4
B. 3 to 2
C. 2 to 1
D. 5 to 1
E. 6 to 1
Part of the project: GRE Quantitative Reasoning Daily Challenge - (2022) EDITION
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GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
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If a code word is defined to be a sequence of different letters chosen
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14 Apr 2022, 05:02
14 Apr 2022, 05:02
Carcass 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
A. 5 to 4
B. 3 to 2
C. 2 to 1
D. 5 to 1
E. 6 to 1
Although we could use the permutation formula to answer this question, we can also solve using the Fundamental Counting Principle (FCP, aka the slot method). In fact, we can solve any permutation question using the FCP.
Number of 5-letter words we can make
We can select the 1st letter in 10 ways
We can select the 2nd letter in 9 ways
We can select the 3rd letter in 8 ways
We can select the 4th letter in 7 ways
We can select the 5th letter in 6 ways
So the total number of ways to construct a 5-letter word = (10)(9)(8)(7)(6)
Number of 4-letter words we can make
We can select the 1st letter in 10 ways
We can select the 2nd letter in 9 ways
We can select the 3rd letter in 8 ways
We can select the 4th letter in 7 ways
So the total number of ways to construct a 4-letter word = (10)(9)(8)(7)
Ratio of the number of 5-letter code words to the number of 4-letter code words = (10)(9)(8)(7)(6)/(10)(9)(8)(7) = 6/1 = 6 to 1
Answer: E
gmatclubot
If a code word is defined to be a sequence of different letters chosen [#permalink]
14 Apr 2022, 05:02
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