Shamhoon wrote: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
let joey be represented by j and frankie by f, here we have five possible cases depending upon the position of joey...!!
1) when joey is at the beginning of the row.!
2) when joey is at the second postion of the row.!
3) when joey is at the third position of the row.!
4) when joey is at the fourth position of the row.!
5) when joey is at the fifth position of the row.!
1) j,_,_,_,_,_. now frankie can choose any of the five vacant positions in 5C1 ways, and the remaining four persons can arrange themselves in 4! ways.
2)_,j,_,_,_,_, here frankie can choose any of the four vacant positions behind the joey, in 4C1 ways, and the remaining four persons can arrange themselves in 4! ways.
3) _,_,j_,_,_. here frankie can choose any of the three vacant positions behind the joey in 3C1 ways,
and the remaining four persons can arrange themselves in 4! ways.
4)_,_,_,j,_,_. here frankie can choose any of the two vacant positions behind the joey in 2C1 ways, and the remaining four persons can arrange themselves in 4! ways.
5)_,_,_,_,j,_ here frankie has only one option of picking up the remaining vacant position behind joey, and remaining four persons can arrange themselves in 4! ways.
hence required no. of ways=5*4!+4*4!+3*4!+2*4!+4!,=15*4!=360.!!
DO Excellence... my search for you is on... you can be far.. but not beyond my reach!
