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Six mobsters have arrived at the theater for the premiere of

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Senior Manager
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Six mobsters have arrived at the theater for the premiere of [#permalink] New post 03 Apr 2008, 14:08
00:00
A
B
C
D
E

Difficulty:

  5% (low)

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0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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
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Re: PS: Combinatorics [#permalink] New post 03 Apr 2008, 17:34
Number of ways to arrange 6 mobsters = 6!
In half of these ways, Frankie will be behind Joey and in the other half, Joey will be behind Frankie.

Answer is D (720/2 = 360)
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Re: PS: Combinatorics [#permalink] New post 03 Apr 2008, 17:42
And if you want to use factorials

IF Joey is 1st, then number of arrangements = 5! = 120
IF Joey is 2nd, then number of arrangements = 5! - 4! = 96
IF Joey is 3rd, then number of arrangements = 5! - 2*4! = 72
IF Joey is 4th, then number of arrangements = 5! - 3*4! = 48
IF Joey is 5th, then number of arrangements = 4! = 24

Total arrangements = 360
Re: PS: Combinatorics   [#permalink] 03 Apr 2008, 17:42
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Six mobsters have arrived at the theater for the premiere of

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