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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