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

Question

Jaelynn Villa

Social Studies

28 February, 09:50

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

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Gianni Morrow · Answer 1

Total arrangement of 6 = 6!.

In half of the cases Frankie will be behind Joey and in half of the cases Joey will be behind Frankie (as probability doesn't favor any of them).

So, the needed arrangement is 6!/2 = 360.