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Probability

by crazy4gmat » Sun Nov 02, 2008 8:03 am
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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by dmateer25 » Sun Nov 02, 2008 8:47 am
Here are the possibilities:

FJ----
F-J---
F--J--
F---J-
F----J
-FJ---
-F-J--
-F--J-
-F---J
--FJ--
--F-J-
--F--J
---FJ-
---F-J
----FJ

So there are 15 ways that Joey can be behind Frankie.

Now the other 4 mobsters can be sorted in any of the spots for each of the 15 possibilities:

4! = 24

15 * 24 = 360

IMO D
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Re: Probability

by logitech » Sun Nov 02, 2008 11:39 am
crazy4gmat 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
6 people can sit in row:

6! = 720 different ways

50 % of these ways Frankie will be in behind Joey

720/2 = 360

if you get confused about this approach you can test it with simple sets like 2 person A and B

A B
B A

there are 2 ways and 1 time A is behind B and 1 time B is behing A ( 50 % )
LGTCH
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by sanju09 » Thu Apr 16, 2009 5:43 am
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.

Source MGMAT

Go with D.
Last edited by sanju09 on Thu Apr 16, 2009 11:58 pm, edited 1 time in total.
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by Ian Stewart » Thu Apr 16, 2009 8:35 am
sanju09 wrote: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.
Sanju, that is word-for-word the explanation provided by MGMAT. It was reprinted in this thread, for example:

www.beatthegmat.com/manhattan-gmat-comb ... t9284.html

Since you have not cited the source of the explanation, you've made it appear that it is your own work and wording. This is normally considered plagiarism. If you are going to quote from a published source, you should credit that source.
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by sanju09 » Thu Apr 16, 2009 11:56 pm
Oh yes Ian! Thanks for telling me the source, which I never knew. Actually one of my student at New Jersy sent me a bunch of questions, few with answers and few with explanations, and demanded my own explanations on the same questions, a month ago. This question was among those with the same explanation, and I liked it better than my own. I can redirect the same mail to you for verification if you want to see it, and you will find that there is no source mentioned in the mail. Now, since I know it by you, I am going to attribute it to MGMAT.

Thanks...
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