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Selection Problem

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Selection Problem

by akshatgupta87 » Thu Apr 21, 2011 9:28 pm
Q.) 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
Someone explain...
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by vineeshp » Thu Apr 21, 2011 9:48 pm
Solutions are gone.

According to a solution given by a previous BTG member, the simple way of thinking here is that, if they are arrange, there are a total of 720 ways of arranging 6 people.

By logic, this set contains half cases where Frankie is ahead of Joey and half where Frankie is behind Joey.

So desired result is 720/2 = 360.
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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by Anurag@Gurome » Thu Apr 21, 2011 9:52 pm
akshatgupta87 wrote:Q.) 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
Someone explain...
No. of ways to arrange sic mobsters = 6! = 6 * 5 * 4 * 3 * 2 = 720 ways
In 50% of 720 ways = 360 ways, Frankie will be behind Joey, and in 360 ways Joey will be behind Frankie.
So, the correct answer is D.
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by vineeshp » Thu Apr 21, 2011 9:57 pm
Another method.

_ _ _ _ _ _

1st 2nd 3rd 4th 5th 6th

Joey can take 1st - 5th position.

Joey 1st:
Remaining 5 can fill in 5! ways: 120 ways.

Joey 2nd
First Seat can be filled by everyone but Frankie and rest can be filled in 4! ways.
4 * 24 = 96.

Joey 3rd
First 2 seats can be filled by 4 * 3 ways (without Frankie in them)
remaining 3 seats 3! ways. Total 12 * 6 = 72 ways

Joey 4th.
Frankie takes 5th or 6th
4 seats can be filled in 4! ways and Frankie can take one of the two behind.
4! * 2 = 48

Joey takes 5th,
Then Frankie takes 6th
Remaining 4 in 4! ways
24 ways

Total is 360.
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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