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
The OA in the post above is incorrect.
The correct answer is
D.
There are 6! = 720 total ways to arrange the 6 mobsters.
Now let's think about this.
Isn't the probability that Frankie will be behind Joey the same as the probability that Joey will be behind Frankie?
Implication:
In 1/2 * 720 = 360 of the arrangements, Frankie will be behind Joey.
In 1/2 * 720 = 360 of the arrangements, Joey will be behind Frankie.
Thus, there are 360 ways in which Frankie can be placed behind Joey.
The correct answer is
D.
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