Jim F.

asked • 11/09/19

Five books labelled A, B, C, D, and E are to be arranged on a shelf. In how many ways can we rearrange these books so that A and C are together?

Five books labelled A, B, C, D, and E are to be arranged on a shelf. In how many ways can we rearrange these books so that A and C are together?


(A) 120 (B) 48 (C) 24 (D) 8 (E) 10

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William W. answered • 11/09/19

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So, 24 possibilities as AC and another 24 possibilities as CA making 48

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Yves S.

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With AC being together, you really have 4 elements ("AC" become only one, with B,D,E being the other three) . The number of permutations of 4 elements out of 4 = PERMUT(4,4) = 24. Doubling to create "CA" the second option, and you get 24+24 = 48. Just as William illustrated above.
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11/09/19

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