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How many different arrangements are possible to place seven different

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How many different arrangements are possible to place seven different  [#permalink]

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New post 06 Jul 2015, 09:37
1
6
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

60% (01:20) correct 40% (01:22) wrong based on 177 sessions

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How many different arrangements are possible to place seven different books on a shelf if all three math books must be placed next to each other?

A. 120
B. 148
C. 360
D. 540
E. 720

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How many different arrangements are possible to place seven different  [#permalink]

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New post 06 Jul 2015, 09:51
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reto wrote:
How many different arrangements are possible to place seven different books on a shelf if all three math books must be placed next to each other?

A. 120
B. 148
C. 360
D. 540
E. 720


Let the 3 math books be \(M_1, M_2, M_3\) while the rest be A,B,C,D for a total of 7 different books.

Consider 3 math books to be 1 collective item (=\(M_1M_2M_3\) = M , as they need to be together). Thus, number of arrangements of 3 different books (\(M_1M_2M_3\))= 3P3 = 3!

Total number of arrangements of M,A,B,C,D = 5P5= 5!

Thus, The total possible arrangements will be : \(M_1M_2M_3ABCD\) = 5!*3! = 720, E is the correct answer.
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Re: How many different arrangements are possible to place seven different  [#permalink]

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New post 09 Oct 2016, 10:45
reto wrote:
How many different arrangements are possible to place seven different books on a shelf if all three math books must be placed next to each other?

A. 120
B. 148
C. 360
D. 540
E. 720


Well said and very easy to follow - The GMATClub Math Book is an excellent study tool, especially for the formulas for this type of problem.
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Re: How many different arrangements are possible to place seven different  [#permalink]

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New post 17 Nov 2016, 17:26
For this one: Combination Total = 4! x 5C1 x 3! = 720
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Re: How many different arrangements are possible to place seven different  [#permalink]

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New post 20 Feb 2018, 07:29
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