Permutation & Combination

[reply2spg]

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

Please explain

SPOILER: OA D

[go2gaurav]

In the given question we have 6 people

All of them can arrange themselves in 6! ways.

We want Joey ahead of Frankie in all the cases.

Out of 6! cases, in half cases Johey will be ahead of Frankie and similarly in rest half he will be behind Frankie.

Hence our answer is 6!/2 = 360.