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Six mobsters have arrived at the theater for the premiere of

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Manager
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Joined: 14 Mar 2014
Posts: 149

Kudos [?]: 173 [0], given: 124

GMAT 1: 710 Q50 V34
Re: Six mobsters have arrived at the theater [#permalink]

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New post 10 Aug 2015, 08:39
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
_________________

I'm happy, if I make math for you slightly clearer
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Kudos [?]: 173 [0], given: 124

Intern
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Joined: 27 Apr 2015
Posts: 33

Kudos [?]: 19 [0], given: 31

Location: India
GMAT 1: 730 Q50 V40
WE: Operations (Telecommunications)
Re: Six mobsters have arrived at the theater for the premiere of [#permalink]

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New post 31 Aug 2015, 21:38
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

Kudos [?]: 19 [0], given: 31

Intern
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Joined: 11 Dec 2012
Posts: 36

Kudos [?]: [0], given: 59

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

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New post 01 Sep 2015, 03:27
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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Kudos [?]: [0], given: 59

Manager
Manager
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B
Joined: 18 Sep 2015
Posts: 109

Kudos [?]: 35 [0], given: 612

GMAT 1: 610 Q43 V31
GMAT 2: 610 Q47 V27
GMAT 3: 650 Q48 V31
GMAT 4: 700 Q49 V35
WE: Project Management (Health Care)
GMAT ToolKit User
Re: Six mobsters have arrived at the theater for the premiere of [#permalink]

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New post 24 May 2016, 14:51
reply2spg wrote:
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


We can pick 2 place for Frankie and Joey (2 of 6) and multiply by the other 4! possiblity for the rest.
(6!/2!*4!)*4!=360.

Kudos [?]: 35 [0], given: 612

Intern
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Joined: 01 Sep 2016
Posts: 9

Kudos [?]: 1 [0], given: 40

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

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New post 07 Jul 2017, 12:29
If they could seat anywhere the answer would be 6! = 720
If one had to seat right behind the other it would be 5! = 120

But we know that there are variations on which other people are seating between them, so the answer must be 120 < x < 720

The only option that fits is D (360)

Kudos [?]: 1 [0], given: 40

Re: Six mobsters have arrived at the theater for the premiere of   [#permalink] 07 Jul 2017, 12:29

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