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How many ways can 6 people be lined up to get on the bus. If certain 2 people refuse to follow each other how many ways are possible?

 Apr 13, 2020
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There are 2! = 2 ways to arrange the 2 refuseniks.

There are 4! = 24 ways to arrange the other 4.

Multiplying these together, we get 48 ways.

 

There are 10 different places to put the refuseniks:  (X = refusenik; - = other)

          X-X---          -X-X--          --X-X-          ---X-X

          X--X--          -X--X-          --X--X

          X---X-          -X---X

          X----X

 

10 x 48  =  480 ways.

 Apr 13, 2020

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