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(1)10 chairs are arranged evenly around King Arthur's round table. In how many ways can 10 knights be seated in the chairs, if Sir Lancelot and Sir Gawain insist on being seated diametrically opposite each other?

 

(2) 

Now suppose that not only must Sir Lancelot and Sir Gawain be diametrically opposite, but Sir Galahad and Sir Percival also demand to be diametrically opposite. How many seatings of the 10 knights are possible?

 

Thanks :)

 Mar 28, 2020
edited by PushyCake  Mar 28, 2020
 #1
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(1): Fix both of them first..the others can sit in 8!=40320 ways is the answer.

 Mar 29, 2020
 #2
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(2) There are 8!*2*2 = 161280 ways of seating the 10 knights.

 Mar 29, 2020

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