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the number of different sequences of 5 letters from an alphabet of 26

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Carcass
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the number of different sequences of 5 letters from an alphabet of 26 [#permalink] New post   Updated on: 09 Apr 2026, 09:43
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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


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Official Answer
A

Originally posted by Carcass on 14 Apr 2022, 02:00.
Last edited by Carcass on 09 Apr 2026, 09:43, edited 1 time in total.
Fixed OA
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Re: the number of different sequences of 5 letters from an alphabet of 26 [#permalink] New post   25 Apr 2022, 09:10
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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
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shvndry
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Re: the number of different sequences of 5 letters from an alphabet of 26 [#permalink] New post   17 Apr 2022, 10:46
How option B is an answer?
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Re: the number of different sequences of 5 letters from an alphabet of 26 [#permalink] New post   17 Apr 2022, 11:15
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For Quantity A, there are 26 choices of letter for each of the 5 spaces in the sequence, for a total of 26 x 26 x 26 x 26 x 26 \(= 11,881,376\) possibilities.
For Quantity B, there are io choices of digit for each of the 8 spaces, for a total of \(10^8 =100,000,000\) possibilities.
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kirishima29
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Re: the number of different sequences of 5 letters from an alphabet of 26 [#permalink] New post   25 Apr 2022, 08:43
shouldn't it be 26C5 x 5! ?? because if it is 26 x 26 x...., then sequences are bound to be repeated, and then the sequences can no longer be distinctive.
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mjhoon104
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Re: the number of different sequences of 5 letters from an alphabet of 26 [#permalink] New post   13 Nov 2025, 02:25
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For A, it should be 26 x 25 x 24 x 23 as it said "different" sequence. It means the sequence cannot be A A A A - every letter has to be different.

As for B, it should 9 x 9 x 8 x 7 x 6 x 5 x 4 x 3 based on the same concept of "different" sequence.
The reason why the first digit is a 9 as opposed to 10 is because the first digit cannot be a 0.
we have 1 2 3 4 5 6 7 8 9 0 to choose from. But the first digit cannot be a 0 so we have 9 options.
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Re: the number of different sequences of 5 letters from an alphabet of 26 [#permalink] New post   09 Apr 2026, 09:38
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Please update this question, the comments hsve clearly demonstrated the answer to be A
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Re: the number of different sequences of 5 letters from an alphabet of 26 [#permalink] New post   09 Apr 2026, 09:43
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Done.

Thank you so much
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Re: the number of different sequences of 5 letters from an alphabet of 26 [#permalink]
09 Apr 2026, 09:43
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