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
How many different arrangements are possible to place seven
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Let the 3 math books = A, B, C and the remaining 4 books = D, E, F, G.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
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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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.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
Answer: E
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