Seven children are going to sit in seven chairs in a row

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Seven children are going to sit in seven chairs in a row [#permalink]

28 Jan 2013, 15:14

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Question Stats:

83% (02:31) correct

16% (00:54) wrong

based on 43 sessions

Seven children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Child A has to sit next to both B & G, with these two children immediately adjacent to Child A on either side. The other four children can sit in any order in any of the remaining seats. How many possible configurations are there for the children?
(A) 240
(B) 480
(C) 720
(D) 1440
(E) 3600

For an in-depth discussion of counting questions such as this one, as well as the complete solution to this question, see:
http://magoosh.com/gmat/2013/gmat-count ... trictions/

[Reveal] Spoiler: OA

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Re: Seven children are going to sit in seven chairs in a row [#permalink]

28 Jan 2013, 15:37

First we can imagine the trio ABG as one item to arrange along with four other items: C , D, E, F.

This can be done in 5! = 120 ways

However the trio can be arranged in 2 ways: BAG or GAB.

So, total number of ways to sit the seven children is equal to 2*120 = 240 (option A)

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Re: Seven children are going to sit in seven chairs in a row [#permalink]

29 Jan 2013, 07:14

Arrange B A and G in the following way --> BAG---- (4 open slots available after BAG). The total number of ways of arranging while fixing BAG in their spots is 4!. Since B and G can be interchanged we have 4!x2 number of ways having B A and G occupying the first 3 slots. Since there are 5 different ways to have A in the middle of B and G the total number of ways of arranging the children is (4!x2) x 5 = 240 (A)

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Re: Seven children are going to sit in seven chairs in a row [#permalink]

29 Jan 2013, 11:28

+1 A

Here, we have to use the glue-method: Suposse that BAG or GAB are just one child. Let's call it X.
So, we have: X, C, D, E, F: Just 5 kids.
We arrange them: 5! =120

Then, we have combinations like this:
X - C -D - E -F
C - X - D - E - F
etc...

But X can be B-A-G or G-A-B
Then: 120 * 2 = 240

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Re: Seven children are going to sit in seven chairs in a row [#permalink]

02 Feb 2013, 05:00

Is this really a 700 question? seemed too easy

Re: Seven children are going to sit in seven chairs in a row [#permalink] 02 Feb 2013, 05:00

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Seven children are going to sit in seven chairs in a row

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Seven children are going to sit in seven chairs in a row

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