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# Permutations problem

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Intern
Joined: 04 Oct 2011
Posts: 2

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10 Oct 2011, 10:20
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Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 5 sessions

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Hi there everyone,

Was wondering if someone could help me with a permutations question.

Six children, Arya, Betsy, Chen, Daniel, Emily and Franco, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?

A) 240
B) 480
C) 540
D) 720
E) 840

I figured that if it wasn't for the condition, the answer would be 6!. There are 10 ways Besty and Emily could be next to each other (5 ways BE, and 5 ways EB). So 6!/10=72 but it's not one of the answers.

The other way I can think of solving it would be to do 6! - 2(5!) which gives 480, a possible option. My reasoning here would be 6! is the total options, minus the number of permutations if we clumped EB or BE together.

If anyone can make this a bit clearer to me it would be very greatly appreciated!

Cheers,
Francis

Cheers,
Francis

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Retired Moderator
Joined: 20 Dec 2010
Posts: 1836

### Show Tags

10 Oct 2011, 11:39
packeted wrote:
Hi there everyone,

Was wondering if someone could help me with a permutations question.

Six children, Arya, Betsy, Chen, Daniel, Emily and Franco, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?

A) 240
B) 480
C) 540
D) 720
E) 840

I figured that if it wasn't for the condition, the answer would be 6!. There are 10 ways Besty and Emily could be next to each other (5 ways BE, and 5 ways EB). So 6!/10=72 but it's not one of the answers.

The other way I can think of solving it would be to do 6! - 2(5!) which gives 480, a possible option. My reasoning here would be 6! is the total options, minus the number of permutations if we clumped EB or BE together.

If anyone can make this a bit clearer to me it would be very greatly appreciated!

Cheers,
Francis

Cheers,
Francis

You have posted the question in the wrong forum. It should have been posted in the PS sub-forum.

*******************************************************
List of forums below. Please subscribe to each of these forums separately.

 ! Please post PS questions in the PS sub-forum: gmat-problem-solving-ps-140/Please post DS questions in the DS sub-forum: gmat-data-sufficiency-ds-141/No posting of PS/DS questions is allowed in the main Math forum.

 ! Critical Reasoning(CR): gmat-critical-reasoning-cr-139/Reading Comprehension(RC): gmat-reading-comprehension-rc-137/Sentence Correction(SC): gmat-sentence-correction-sc-138/Analytical Writing And Assessment: analytical-writing-assessment-awa-144/Please DO NOT post any question in main Verbal forum:verbal-gmat-questions-11/

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 49858

### Show Tags

23 Oct 2017, 03:38
packeted wrote:
Hi there everyone,

Was wondering if someone could help me with a permutations question.

Six children, Arya, Betsy, Chen, Daniel, Emily and Franco, are to be seated in a single row of six chairs. If Betsy cannot sit next to Emily, how many different arrangements of the six children are possible?

A) 240
B) 480
C) 540
D) 720
E) 840

I figured that if it wasn't for the condition, the answer would be 6!. There are 10 ways Besty and Emily could be next to each other (5 ways BE, and 5 ways EB). So 6!/10=72 but it's not one of the answers.

The other way I can think of solving it would be to do 6! - 2(5!) which gives 480, a possible option. My reasoning here would be 6! is the total options, minus the number of permutations if we clumped EB or BE together.

If anyone can make this a bit clearer to me it would be very greatly appreciated!

Cheers,
Francis

Cheers,
Francis

OPEN DISCUSSION OF THIS QUESTION IS HERE: six-children-arya-betsy-chen-daniel-emily-and-franco-are-to-be-210939.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________
Re: Permutations problem &nbs [#permalink] 23 Oct 2017, 03:38
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