Six mobster

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Six mobster

by gmatplayer » Sun Aug 16, 2009 3:05 pm
This is the first time I am posting question from one of the well-known test I bought & took yesterday. I do not know whether it is against copyright or not. If it is, I will not do it again.

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







OA (D)

Can anybody explain this? My answer was 153 (5! + 4! + 3! + 2! + 1!)
Source: — Problem Solving |

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by tohellandback » Sun Aug 16, 2009 5:50 pm
the positions are
1 2 3 4 5 6
Joey can take any place from 1 to 5
when Joey is at 1:
Frankie can take any place from 2 to 6=5 places
other members can arrange themselves in 4! ways
total=4!* 5=120
same way when Joey is at 2: 4!*4=96 ways
same way when Joey is at 3: 4!*3=72 ways
same way when Joey is at 4: 4!*2=48 ways
same way when Joey is at 5: 4!=24 ways

total=120+96+72+48+24=360 ways
The powers of two are bloody impolite!!

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by gmatplayer » Sun Aug 16, 2009 6:11 pm
Thanks tohellandback. Seems not so tough, but in those 2min....well, you know