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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?

 Jun 23, 2020
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(1) There are 36288 ways

 

(2) There are 12096 ways.

 Jun 24, 2020

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