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# Six mobsters have arrived at the theater for the premiere of

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Senior Manager
Joined: 20 Dec 2004
Posts: 251

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Six mobsters have arrived at the theater for the premiere of [#permalink]

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03 Apr 2008, 15:08
00:00

Difficulty:

(N/A)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 4 sessions

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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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Kudos [?]: 112 [0], given: 0

Current Student
Joined: 27 Mar 2008
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Schools: Kellogg Class of 2011

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03 Apr 2008, 18:34
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)

Kudos [?]: 45 [0], given: 1

Current Student
Joined: 27 Mar 2008
Posts: 415

Kudos [?]: 45 [0], given: 1

Schools: Kellogg Class of 2011

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03 Apr 2008, 18:42
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

Kudos [?]: 45 [0], given: 1

Re: PS: Combinatorics   [#permalink] 03 Apr 2008, 18:42
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