Six mobsters have arrived at the theater for the premiere of

[Sage Pearce-Higgins]

Thanks for detailing your logic. Let me approach a few points separately. First, the phrase 'not necessarily right behind him' means that Frankie is going to be behind Joey, possibly right behind him, or possibly with a gap between. This phrase certainly doesn't mean 'not right behind him'. If I asked you to buy me some cake, think of the difference between me saying 'not necessarily chocolate' and 'not chocolate'.

that led me to him being able to be in four spots (4!) but not in two spots (2!), out of six spots (numerator)

Unfortunately this isn't the right way to translate that situation into numbers. We can't simply divide by (the number of spots Joey can be in)! x (the number Joey can't be in)!. Think: this would mean that if Joey could be in all six spots, then we'd divide by 6! and there would be only one possibility - nonsense! I think you're mixing this up with something else: if we order objects and some of the objects are the same, then we divide by the factorial of that number. For more on this check out chapter 4 of the Number Properties Strategy Guide.

[JackF968]

So helpful. Thank you. I can't believe I missed the "necessarily." All I can say going forward is, "oh boy."

[Sage Pearce-Higgins]

Enjoy your mistakes - they'll help you learn.