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There are 8 identical chairs around a circular table. In how many ways can 5 people be seated in 5 of these chairs if Richard wants to sit next to Surya, but doesn't want to sit next to Tamas?

(Consider two seating arrangements to be the same if one seating arrangement can be rotated to obtain the other.)


there is 8! ways to seat the 5 people but that does not fit the requirement of the question

 Aug 9, 2022
 #1
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Sit Richard in any chair

 

Surya can occupy any  one of two positions (either to his right or left)   =  2

 

Tamas  then can occupy  any one of five remaining positions =   5

 

And the other two people  can occupy the other positions in  P(5,2) ways  =  20

 

So

 

2 * 5 * 20  =    200 ways

 

 

cool cool cool

 Aug 9, 2022

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