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Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6

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gmihir
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Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 [#permalink] New post   15 Apr 2012, 21:16
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Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?

A. 360
B. 120
C. 80
D. 240
E. 60
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Bunuel
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Re: Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 [#permalink] New post   16 Apr 2012, 00:58
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gmihir wrote:
Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?

A. 360
B. 120
C. 80
D. 240
E. 60


Total # of arrangement of 6 people is 6!.

In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).

So, # of arrangements to satisfy the given condition is 6!/2=360.

Answer: A.

Similar questions to practice:
in-how-many-different-ways-can-the-letters-a-a-b-91460.html
six-mobsters-have-arrived-at-the-theater-for-the-premiere-of-the-126151.html

Hope it helps.
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ind23
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Re: Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 [#permalink] New post   12 Apr 2014, 01:19
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satsymbol wrote:
Why Can not I use Glue method here?
SK together, with 4 others - 5! = 120 ways.




Hi,

When you are using the above method what you are assuming is that they are sitting next to each other always, which is not what the question states.
The question only says that S is always sitting left of T, maybe next, maybe away 1 chair ...there is no constraint on that.

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Re: Permutations [#permalink] New post   15 Apr 2012, 22:57
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Total number of arrangements = 6! = 720

In exactly half, Susan will be to the left of Tim, which gives us 360 arrangements

Option (A)
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satsymbol
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Re: Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 [#permalink] New post   11 Apr 2014, 19:47
Why Can not I use Glue method here?
SK together, with 4 others - 5! = 120 ways.
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Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 [#permalink] New post   Updated on: 30 Nov 2023, 09:14
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gmihir wrote:
Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?

A. 360
B. 120
C. 80
D. 240
E. 60


This post discusses the symmetry concept: https://anaprep.com/combinatorics-linea ... -symmetry/

Originally posted by KarishmaB on 24 Jun 2015, 21:53.
Last edited by KarishmaB on 30 Nov 2023, 09:14, edited 1 time in total.
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Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 [#permalink] New post   13 Dec 2020, 11:35
Given: Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 identical chairs in straight line so that Susan is seated always left to Tim.
Asked: How many such arrangements are possible ?

Total arrangements possible = 6! = 720
In half of the arrangements Susan is seated left to Tim, number of arrangements so that Susan is seated always left to Tim = 720/2 = 360

IMO A
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Re: Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 [#permalink] New post   11 Feb 2024, 09:38
Hello from the GMAT Club BumpBot!

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Re: Susan, John, Daisy, Tim, Matt and Kim need to be seated in 6 [#permalink]
11 Feb 2024, 09:38
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