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by thephoenix » Thu Feb 04, 2010 9:04 pm
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
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by Osirus@VeritasPrep » Thu Feb 04, 2010 9:13 pm
I think its 120 but I'm not sure. The answer should be 5!

If Joey is at the front Frankie has 5 options
If Joey is at seat 2 Frankie has 4 options
If Joey is at seat 3 Frankie has 3 options
If Joey is at seat 4 Frankie has 2 options
If Joey is at seat 5 Frankie has 1 option

5 * 4 * 3 * 2 * 1 = 120
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by papgust » Thu Feb 04, 2010 9:19 pm
I would go for D

Total combinations in which six mobsters could be arranged is 6! = 720.

50% chances are that Frankie could sit behind Joey. So, 1/2 * 720 = [spoiler]360 (D)[/spoiler]
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by neelimareddym » Thu Feb 04, 2010 9:26 pm
Total number of combinations

J __ __ __ __ __ --> 5
__ J __ __ __ __ --4
__ __ J __ __ __ -->3
__ __ __ J __ __ --> 2
__ __ __ __ J __ -- >1

Total number of combinations = 5*4*3*2*1 = 120


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by ajith » Thu Feb 04, 2010 11:42 pm
thephoenix 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?
6
24
120
360
720
if We fix joey in first position, Frankie can take 5 positions after Frankie takes position others can take positions in 4! ways
if We fix joey in Second position, Frankie can take 4 positions after Frankie takes position others can take positions in 4! ways...
....
So on and so forth

Total number of ways =

5*4! + 4*4! +3*4! + 2*4! +4!)
(5+4+3+2+1)*4!

= 6*5/2*4! = 360
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by thephoenix » Fri Feb 05, 2010 12:32 am
ajith wrote:
thephoenix 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?
6
24
120
360
720
if We fix joey in first position, Frankie can take 5 positions after Frankie takes position others can take positions in 4! ways
if We fix joey in Second position, Frankie can take 4 positions after Frankie takes position others can take positions in 4! ways...
....
So on and so forth

Total number of ways =

5*4! + 4*4! +3*4! + 2*4! +4!)

oh man!!!!!!!!
i came mentally till here and then left looking onto the ans....i thought i am way away from soln..........(mental block)
thanks for removing my mental block
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