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How many different arrangements are possible to place seven

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by AAPL » Fri Feb 22, 2019 4:07 am

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Economist GMAT

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

OA E
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by GMATGuruNY » Fri Feb 22, 2019 4:59 am
AAPL wrote:Economist GMAT

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 = A, B, C and the remaining 4 books = D, E, F, G.
Since the 3 math books must be next to one another, put them together in a block:
[ABC].
The number of ways to arrange the 5 elements [ABC], D, E, F and G = 5! = 120.
Since A, B and C can swap positions within the [ABC] block, the result above must be multiplied by the number of ways to arrange A, B and C within the block (3!):
120 * 3! = 720.

The correct answer is E.
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by Scott@TargetTestPrep » Sun Feb 24, 2019 5:32 am
AAPL wrote:Economist GMAT

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

OA E
Let's think of the three math books as a single group. Then, the four non-math books together with the group of math books can be arranged in 5! = 120 ways. Within the group, the three math books can be arranged in 3! = 6 ways; therefore, a total of 120 x 6 = 720 arrangements are possible.

Answer: E

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