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the number of different sequences of 5 letters from an alphabet of 26
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Updated on: 09 Apr 2026, 09:43
Updated on: 09 Apr 2026, 09:43
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Question Stats:
56% (01:20) correct
43% (01:39) wrong based on 69 sessions
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Quantity A |
Quantity B |
the number of different sequences of 5 letters from an alphabet of 26 letters |
the number of different sequences of 8 digits |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
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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Posts: 6218
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Re: the number of different sequences of 5 letters from an alphabet of 26
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25 Apr 2022, 09:10
25 Apr 2022, 09:10
4
Carcass wrote:
Quantity A |
Quantity B |
the number of different sequences of 5 letters from an alphabet of 26 letters |
the number of different sequences of 8 digits |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
In my opinion, the wording of this question is too ambiguous for the question to ever be an official GRE question.
Here's my interpretation:
QUANTITY A: Since we're asked for sequences of 5 letters, I'm assuming that those five letters are all different
If that's the case, then there are:
26 options for the first letter
25 options for the second letter
24 options for the third letter
23 options for the fourth letter
22 options for the fifth letter
So, by the fundamental counting principle (FCP), the total number of 5-letter sequences = (26)(25)(24)(23)(22)
QUANTITY B: Since we're asked for sequences of 8 digits, I'm assuming that those 8 digits are all different.
I'm also going to assume that the first digit can be 0.
If that's the case, then there are:
10 options for the first digit
9 options for the second digit
8 options for the third digit
7 options for the fourth digit
6 options for the fifth digit
5 options for the sixth digit
4 options for the seventh digit
3 options for the eighth digit
So, by the fundamental counting principle (FCP), the total number of 8- digit sequences = (10)(9)(8)(7)(6)(5)(4)(3)
So we have:
QUANTITY A: (26)(25)(24)(23)(22)
QUANTITY B: (10)(9)(8)(7)(6)(5)(4)(3)
Answer: A
General Discussion
Re: the number of different sequences of 5 letters from an alphabet of 26
[#permalink]
17 Apr 2022, 10:46
17 Apr 2022, 10:46
How option B is an answer?
