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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
Posts: 464
Concentration: Marketing, Finance
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Re: Six mobsters have arrived at the theater for the premiere of [#permalink]

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27 Dec 2012, 23:05
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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]

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28 Feb 2013, 10:57
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]

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01 Apr 2014, 07:47
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Re: Six mobsters have arrived at the theater for the premiere of [#permalink]

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23 May 2015, 16:52
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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Six mobsters have arrived at the theater [#permalink]

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10 Aug 2015, 08:24
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]

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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
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I'm happy, if I make math for you slightly clearer
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Re: Six mobsters have arrived at the theater for the premiere of [#permalink]

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

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

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24 May 2016, 14:51
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.
Intern
Joined: 12 Dec 2016
Posts: 13
Manhattan freePrep combination question - can't understand ! [#permalink]

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12 Dec 2016, 13:53
Heyhey!

This is my first ever post here. I have my gmat at 19th of December and need to pass 600 limit, however i had in total 18 days to study and i really do not believe in myself do pass 600 limit, since i had almost 0 math knowledge left ... thanks to my university.
Anyway; this is the question From manhattan freePrep test)

"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?"

Solution:

"Ignoring Frankie's requirement for a moment, observe that the six mobsters can be arranged 6! or 6 x 5 x 4 x 3 x 2 x 1 = 720 different ways in the concession stand line. In each of those 720 arrangements, Frankie must be either ahead of or behind Joey. Logically, since the combinations favor neither Frankie nor Joey, each would be behind the other in precisely half of the arrangements. Therefore, in order to satisfy Frankie's requirement, the six mobsters could be arranged in 720/2 = 360 different ways."

Where i don't understand:

It says that Frankie has to stay behind Joey, however in the answer it explicitly says that Frankie must be either ahead of or behind Joey.

This part really contradicts each other, and there is no way i can extract any logic from the question yet begin the process of solving.
I'd love to hear some advices from experts

Kind regards,
Mesut Törün
Math Expert
Joined: 02 Sep 2009
Posts: 39626
Re: Six mobsters have arrived at the theater for the premiere of [#permalink]

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12 Dec 2016, 13:58
mesutthefail wrote:
Heyhey!

This is my first ever post here. I have my gmat at 19th of December and need to pass 600 limit, however i had in total 18 days to study and i really do not believe in myself do pass 600 limit, since i had almost 0 math knowledge left ... thanks to my university.
Anyway; this is the question From manhattan freePrep test)

"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?"

Solution:

"Ignoring Frankie's requirement for a moment, observe that the six mobsters can be arranged 6! or 6 x 5 x 4 x 3 x 2 x 1 = 720 different ways in the concession stand line. In each of those 720 arrangements, Frankie must be either ahead of or behind Joey. Logically, since the combinations favor neither Frankie nor Joey, each would be behind the other in precisely half of the arrangements. Therefore, in order to satisfy Frankie's requirement, the six mobsters could be arranged in 720/2 = 360 different ways."

Where i don't understand:

It says that Frankie has to stay behind Joey, however in the answer it explicitly says that Frankie must be either ahead of or behind Joey.

This part really contradicts each other, and there is no way i can extract any logic from the question yet begin the process of solving.
I'd love to hear some advices from experts

Kind regards,
Mesut Törün

Merging topics. Please refer to the previous discussion.

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Re: Six mobsters have arrived at the theater for the premiere of   [#permalink] 12 Dec 2016, 13:58

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

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