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Joey And Frankie

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Joey And Frankie

by cypherskull » Sun Aug 26, 2012 4:43 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?
a.6
b.24
c.120
d.360
e.720
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by Brent@GMATPrepNow » Sun Aug 26, 2012 6:06 am
cypherskull 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?
a.6
b.24
c.120
d.360
e.720
If we remove the restriction that Frankie must stand behind Joey, then the 6 mobsters can be arranged in 6! (720) different ways.

Now, of these 720 different arrangements, it is clear that Frankie will be standing behind Joey half the time, and Joey will be standing behind Frankie half the time.

So, the answer is 720/2 or 360 or D.

Extension: If there were n mobsters, then the answer would be n!/2

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Brent
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