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# How many different arrangements are possible to place seven different

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Retired Moderator
Joined: 29 Apr 2015
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Concentration: Economics, Finance
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How many different arrangements are possible to place seven different  [#permalink]

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06 Jul 2015, 10:37
1
6
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Difficulty:

55% (hard)

Question Stats:

61% (01:19) correct 39% (01:21) wrong based on 183 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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06 Jul 2015, 10:51
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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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Joined: 07 Jun 2016
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Re: How many different arrangements are possible to place seven different  [#permalink]

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09 Oct 2016, 11:45
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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17 Nov 2016, 18:26
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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20 Feb 2018, 08:29
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Re: How many different arrangements are possible to place seven different   [#permalink] 20 Feb 2018, 08:29
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