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Six mobsters

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by GmatKiss » Sun Oct 30, 2011 10:58 am
Six mobsters have arrived at the theater for the premiere of the film "Goodbuddies." 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?
6
24
120
360
720

IMO:120
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by rijul007 » Sun Oct 30, 2011 11:04 am
GmatKiss wrote:Six mobsters have arrived at the theater for the premiere of the film "Goodbuddies." 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?
6
24
120
360
720

IMO:120

i got 360
could you please check your ans again
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by neelgandham » Tue Nov 01, 2011 6:16 am
GmatKiss wrote:Six mobsters have arrived at the theater for the premiere of the film "Goodbuddies." 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?
6
24
120
360
720

IMO:120

J _ _ _ _ _ = 5*4*3*2 = 30*4
_ J _ _ _ _ = 4*4*3*2 = 24*4
_ _ J _ _ _ = 4*3*3*2 = 18*4
_ _ _ J _ _ = 4*3*2*2 = 12*4
_ _ _ _ J _ = 4*3*2*1 = 6*4

Total = 360

Can you please publish the answer ?
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by GmatKiss » Tue Nov 01, 2011 6:20 am
OA: 360
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by shankar.ashwin » Tue Nov 01, 2011 6:25 am
Total possibilities - 6! = 720

In exactly half the arrangements J will be ahead of Frank and in the other half J will be behind Frank.

So, 720/2= 360 possibilities
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