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The probability that a word selected from the set of all rearrangement

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Carcass
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The probability that a word selected from the set of all rearrangement [#permalink] New post   25 Mar 2021, 01:39
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Quantity A
Quantity B
The probability that a word selected from the set of all rearrangements of the letters of the word "Math" results in "Math"
The probability that a word selected from the set of all rearrangements of the letters of the word "Good" results in "Good"



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

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Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
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The probability that a word selected from the set of all rearrangement [#permalink] New post   25 Mar 2021, 02:48
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Carcass wrote:
Quantity A
Quantity B
The probability that a word selected from the set of all rearrangements of the letters of the word "Math" results in "Math"
The probability that a word selected from the set of all rearrangements of the letters of the word "Good" results in "Good"



A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.


Tricky one! - tricked me as well

\(n\) objects can be arranged in a line or a row in \(n!\) ways

"Math" can be arranged in \(4! = 24\) ways

"Good" can be arranged in \(\frac{4!}{2!} = 12\) ways

Now,

Col. A: \(\frac{1}{24}\)
Col. B: \(\frac{1}{12}\)

Multiplying by \(24\) both sides:

Col. A: \(1\)
Col. B: \(2\)

Hence, option B
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Re: The probability that a word selected from the set of all rearrangement [#permalink] New post   25 Mar 2021, 03:14
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And for this very good reason your are the lead moderator after Brent :)
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Re: The probability that a word selected from the set of all rearrangement [#permalink] New post   25 Mar 2021, 03:16
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Carcass wrote:
And for this very good reason your are the lead moderator after Brent :)


Thanks a lot :please:
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The probability that a word selected from the set of all rearrangement [#permalink] New post   26 Mar 2021, 14:36
Good question! There is only one way to spell MATH with the letters we're given. However, there are two ways to spell GOOD: GOOD and GOOD. Thus QB > QA
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Re: The probability that a word selected from the set of all rearrangement [#permalink] New post   24 Aug 2024, 07:57
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The probability that a word selected from the set of all rearrangement [#permalink]
24 Aug 2024, 07:57
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