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

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 % )

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.

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...