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In how many ways can $9$ friends sit at a dinner table if two of them, Anna and Bob, insist on having exactly two people seated between them? (As usual, two seatings are considered the same if one is a rotation of the other.)

HELLLLLLLLLLLLLLLLLPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! I get 5040. Is that right?

Guest Jun 19, 2017
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Anchor Anna and Bob in any two chairs.....and they can be seated in two ways.....the other seven people can be arranged in 7!  = 5040 ways

 

So....

 

2 ways x 5040 ways   =  

 

10,080  arrangements

 

 

cool cool cool

CPhill  Jun 19, 2017

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