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

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Re: Six mobsters have arrived at the theater for the premiere of [#permalink]  27 Dec 2012, 22:05
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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?

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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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]  23 May 2015, 15:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Six mobsters have arrived at the theater for the premiere of   [#permalink] 23 May 2015, 15:52

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