mobsters combination

[PAB2706]

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

[lilu]

https://www.beatthegmat.com/mobsters-t15563.html

[Vemuri]

I am not good with permutation & combinations. But, I will try.

The requirement is that Frankie is always behind Joey, not necessarily immediately behind him. That means Joey cannot be the last person in the line (because Frankie should be behind him). So, Joey can be placed in any of the first five positions in 5 ways.

When Joey is in the
I position, Frankie has 5 ways of standing in the line & the rest can stand in 4! ways, i.e. 5X4X3X2X1 = 120 ways
II position, Frankie has 4 ways of standing in the line & the rest can stand in 4! ways, i.e. 4X4X3X2X1 = 96 ways
III position, Frankie has 3 ways of standing in the line & the rest can stand in 4! ways, i.e. 3X4X3X2X1 = 72 ways
IV position, Frankie has 2 ways of standing in the line & the rest can stand in 4! ways, i.e. 2X4X3X2X1 = 48 ways
V position, Frankie has 1 way of standing in the line & the rest can stand in 4! ways, i.e. 1X4X3X2X1 = 24 ways

Adding all the possibilities = 120+96+72+48+24 = 360ways.

I hope my approach & answer are correct

[PAB2706]

OA is D


Vemuri ur approach is nice.. i was actually looking for this kind of an explanation bcos according to the wording of the problem i interpreted it as frankie shud always be behind joey as frankie wants to keep an eye on joey. the way the test takers have explained it they have concidered tht frankie can be ahead or behind joey and thus halfed the total combination ie 6! /2.

I think ur explanation is the best tht i can understand.[/i]