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There are 5 chairs. Tim and Jack want to sit such that Tim i

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There are 5 chairs. Tim and Jack want to sit such that Tim i [#permalink] New post 31 Jan 2012, 16:45
There are 5 chairs. Tim and Jack want to sit such that Tim is alwalys left to Jack. How many arrangements are possible ?

Is the answer to this question - 10 or 60 ? Could someone please clarify ?

Thanks in advance
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Magoosh GMAT Instructor
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Re: There are 5 chairs. Tim and Jack want to sit such that Tim i [#permalink] New post 31 Jan 2012, 18:20
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There are 5P2 ways they can sit = 20.

In half those instances, Jack will be on the left of Tim (the other half he will be on his right).

Therefore total of 10 different ways.
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Re: There are 5 chairs. Tim and Jack want to sit such that Tim i [#permalink] New post 01 Feb 2012, 00:07
Chris why can't the answer be 60 ( 5 factorial/2) ????
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Re: There are 5 chairs. Tim and Jack want to sit such that Tim i [#permalink] New post 01 Feb 2012, 00:08
Any way chris thanks for your reply.
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Re: There are 5 chairs. Tim and Jack want to sit such that Tim i [#permalink] New post 01 Feb 2012, 13:55
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Hi gpkk,

120 or 5! would represent the total ways you could see 5 people in 5 chairs. We are only sitting 2 in 5 - hence we use the permutations formula, 5P2 = 20, the total number of different ways the two can be arranged in five chairs. Half of those 20 cases Tim is to the left of Jack. Therefore, the answer is 10.

Please let me know if that was any clearer :-D
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Re: There are 5 chairs. Tim and Jack want to sit such that Tim i [#permalink] New post 01 Feb 2012, 22:16
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gpkk wrote:
There are 5 chairs. Tim and Jack want to sit such that Tim is alwalys left to Jack. How many arrangements are possible ?

Is the answer to this question - 10 or 60 ? Could someone please clarify ?

Thanks in advance


The question implies that there are 5 chairs and only 2 people, Tim and Jack. If that is the case, answer will be what Chris explained above. You select 2 chairs out of 5 and make Tim and Jack occupy them.

If instead, the question were that there are 5 chairs and 5 people and that Tim and Jack are 2 of those 5 people, then you are right. The answer would be 5!/2! because 5 people can occupy 5 chairs in 5! ways and Tim will be to the left of Jack in half of them.

For more on such questions, check:
http://www.veritasprep.com/blog/2011/10 ... s-part-ii/
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Re: There are 5 chairs. Tim and Jack want to sit such that Tim i [#permalink] New post 01 Feb 2012, 22:19
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ChrisLele wrote:
Hi gpkk,

120 or 5! would represent the total ways you could see 5 people in 5 chairs. We are only sitting 2 in 5 - hence we use the permutations formula, 5P2 = 20, the total number of different ways the two can be arranged in five chairs. Half of those 20 cases Tim is to the left of Jack. Therefore, the answer is 10.

Please let me know if that was any clearer :-D


Oops! Didn't see this reply before so put down a quick explanation.
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Re: There are 5 chairs. Tim and Jack want to sit such that Tim i [#permalink] New post 06 Mar 2012, 08:59
Thank you guys for these great explanations!
Re: There are 5 chairs. Tim and Jack want to sit such that Tim i   [#permalink] 06 Mar 2012, 08:59
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There are 5 chairs. Tim and Jack want to sit such that Tim i

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