Six mobsters have arrived at the theater for the premiere of the film “Good buddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie’s requirement is satisfied?
A. 6
B. 24
C. 120
D. 360
E. 720
[spoiler]OA=D[/spoiler]
Source: Manhattan GMAT
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Six mobsters have arrived at the theater for the premiere of the film “Good buddies.” One of the mobsters, Frankie, is a
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Solution:Vincen wrote: ↑Wed Jun 24, 2020 1:43 amSix mobsters have arrived at the theater for the premiere of the film “Good buddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in line at the concession stand, though not necessarily right behind him. How many ways can the six arrange themselves in line such that Frankie’s requirement is satisfied?
A. 6
B. 24
C. 120
D. 360
E. 720
[spoiler]OA=D[/spoiler]
We see that we can arrange the 6 mobsters in 6! = 720 ways. Since the number of ways in which Joey stands in front of Frankie is equal to the number of ways he stands behind him, the number of ways that the group can be arranged to satisfy Frankie’s requirement is 720/2 = 360 ways.
Answer: D
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