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Combinatorics Clarification

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frederick.benny
 Post subject: Combinatorics Clarification
 Post Posted: Sat Jun 25, 2011 2:46 am 
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Students


Posts: 2
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?

6
24
120
360
720

I got this one incorrect.

Can someone from the MGMAT team explain this little more elaborately ?

Also can you explain the flaw in my reasoning:
Required Arrangement: 6 people = 6! =720 ways
Constraint: F wants to stand begin J.

Now the only arrangement when F wont be behind J is when J stands at the end of 6 people.
J *5! = 120 ways

So arrangements in which F is always behind J = 720 - 120 = 600 ways, which is not even in the options.

Ideas anyone?
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jnelson0612
 Post subject: Re: Combinatorics Clarification
 Post Posted: Sat Jun 25, 2011 2:02 pm 
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ManhattanGMAT Staff


Posts: 1857
Check out this thread: six-mobsters-have-arrived-at-the-theater-for-the-premiere-of-t739.html

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Jamie Nelson
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