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12 Jan 2009, 03:29
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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
6
24
120
360
720
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12 Jan 2009, 04:26
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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.
The correct answer is D."
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
In that case the answer will be 240 which is not there in your answer choices.
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.
The correct answer is D."
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
In that case the answer will be 240 which is not there in your answer choices.
