Question 349982
6 seats and 6 persons, two of them should not sit together.

No. of ways to arrange 6 person at 6 place without any restriction = 6P6 = 6!
                                               

now, we will find how many ways these two friends can sit together .

assume both are single entity then total 5 person  i.e 4 + (Joey + Ross)

       no. of ways = 5p5 * 2!  ( 2! for arrangement that they can make i.e JR,RJ) 
                    = 5! * 2!

  Now, this value can be subtracted from previous value where was no restriction


     
 total no. of ways = 6! - 5! * 2 

                   = 720 - 240 

                   = 480

   so, total 480 ways.

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