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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!

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Six mobsters have arrived at the theater [#permalink]  10 Aug 2015, 07:24
Six mobsters have arrived at the theater for the premiere of a film. One of the mobsters, Eden, is an informer, and he is afraid that another member of his crew, Costa, is on to him. Eden wanting to keep Costa in his sights, insists upon standing behind Costa in line at the concession stand. how many ways can the six arrange themselves in line such that Eden's requirement is satisfied?

a. 6
b. 24
c. 120
d. 360
e. 720
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Re: Six mobsters have arrived at the theater [#permalink]  10 Aug 2015, 07:39
VenoMfTw wrote:
Six mobsters have arrived at the theater for the premiere of a film. One of the mobsters, Eden, is an informer, and he is afraid that another member of his crew, Costa, is on to him. Eden wanting to keep Costa in his sights, insists upon standing behind Costa in line at the concession stand. how many ways can the six arrange themselves in line such that Eden's requirement is satisfied?

a. 6
b. 24
c. 120
d. 360
e. 720

Half of the total possible ways Costa will be ahead of Eden
And for other half Eden will be ahead of Costa

Total possible ways = 6! = 720 ways

Thus for required = 720/2 =360
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Re: Six mobsters have arrived at the theater for the premiere of [#permalink]  31 Aug 2015, 20:38
Now the method I'm discussing has already been shared, but the explanations were not too clear for me, so sharing a detailed explanation.
Now following can be the available arrangements (please note that the question requires us to place Frankie behind Joey in line, though not necessarily right behind him):
_ _ _ _ _ F: when F is at the last, there are 5 options for J and the rest can be arranged in 4! ways: 5x4!
_ _ _ _ F _: when F is at the second last position, there are 4 options for J and the rest can be arranged in 4! ways: 4x4!
_ _ _ F _ _: when F is at the third last position, there are 3 options for J and the rest can be arranged in 4! ways: 3x4!
_ _ F _ _ _: when F is at the third third spot from the front, there are 2 options for J and the rest can be arranged in 4! ways: 2x4!
_ F _ _ _: when F is at the third third spot from the front, there is only 1 options for J and the rest can be arranged in 4! ways: 4!
Now F can not be placed at the first spot as he has to be behind J, so above are al the situations possible and the sum would give us the total arrangements.
total arrangements = 5x4! + 4x4! + 3x4! + 2x4! + 4! = (5+4+3+2+1)4! = 15x4! = 360
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Six mobsters have arrived at the theater for the premiere of [#permalink]  01 Sep 2015, 02:27
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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Six mobsters have arrived at the theater for the premiere of   [#permalink] 01 Sep 2015, 02:27

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