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

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Senior Manager
Joined: 13 Aug 2012
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Concentration: Marketing, Finance
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Re: Six mobsters have arrived at the theater for the premiere of [#permalink]  27 Dec 2012, 22:05
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

Solution 1:
How many ways to arrange 6 without restriction? 6!
In the total of ways, half of the time J will be behind F or F behind J.
=6!/2 = 360

Solution 2:
To get a little more practice on permutations...

We could count the possibilities of J(...)F.

0 person in between: 5
1 person in between: 4
2 persons in between: 3
3 persons in between: 2
4 persons in between: 1

(5 + 4 + 3 + 2 + 1) * 4! = 360
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Senior Manager
Status: struggling with GMAT
Joined: 06 Dec 2012
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Concentration: Accounting
GMAT Date: 04-06-2013
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Kudos [?]: 94 [0], given: 46

Re: Six mobsters have arrived at the theater for the premiere of [#permalink]  28 Feb 2013, 09:57
thanks to all for explanation.Finally i understand the concept................
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Re: Six mobsters have arrived at the theater for the premiere of [#permalink]  01 Apr 2014, 06:47
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Re: Six mobsters have arrived at the theater for the premiere of   [#permalink] 01 Apr 2014, 06:47
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