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MGMAT _PS-Prob

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Senior Manager
Joined: 05 Jun 2008
Posts: 304

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12 Jan 2009, 02:29
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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?
6
24
120
360
720
Manager
Status: Stanford GSB
Joined: 02 Jun 2008
Posts: 94

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12 Jan 2009, 03:26
I am assuming that Frankie can stand right behind Joey:

One interesting solution from Luci

"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.

If Frankie (F) cannot stand right behind Joey(J):
We have to deduct those no of possibilities where F was right behind J from 360.
The cases are,
F J _ _ _ _
_ F J _ _ _
_ _ F J _ _
_ _ _ F J _
_ _ _ _ F J
In case, the arrangement will be 4*3*2= 24
So we have to deduct 24*5 cases = 120 from 360

Intern
Joined: 22 Nov 2006
Posts: 12

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21 Jan 2009, 05:33
120

F....J = 4! = 24 ways
F...J. = 4! = 24 ways
F..J.. = 24
F.J... = 24
FJ.... = 24

total no of ways = 24*5 = 120
SVP
Joined: 07 Nov 2007
Posts: 1789
Location: New York

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21 Jan 2009, 07:18
1
KUDOS
nagk78 wrote:
120

F....J = 4! = 24 ways
F...J. = 4! = 24 ways
F..J.. = 24
F.J... = 24
FJ.... = 24

total no of ways = 24*5 = 120

you missed other patterns
.F....J
..f....J
etc.

below is the best way to solve.

total number of ways 6 people arranged themselves = 6! =720

Probablity that F is Behind J. =1/2

Total number of ways = 720/2 = 360
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Re: MGMAT _PS-Prob   [#permalink] 21 Jan 2009, 07:18
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