Factorials

[sayahmichelle]

Can someone please clarify the way this question has been solved, I do not understand why we divided by two to get the answer.

Thanks

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

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.

[jnelson0612]

Hi sayahmichelle,
There's a lot of discussion in this thread about why we divide by 2: post3924.html

Please read this thread and if you still don't understand let us know and we're happy to help further.

Thanks!

[sayahmichelle]

Thank you so much, it makes more sense now:)

[tim]

:)