6. Suppose King Arthur and the knights of the round table are sitting at the rou

Question

6. Suppose King Arthur and the knights of the round table are sitting at the round table. Assume that there are n chairs and n knights including King (a) If one of the chairs is a throne and King Arthur sits in the throne, (b) If anyone could sit in the throne, how many seating arrangements (c) If all n chairs are identical, how many seating arrangements are there? Arthur. how many seating arrangements are there? are there? (Assume that if everyone moves one seat clockwise, then the seating arrangement has not changed.) (d) In part (c), what would be a good way to uniquely describe n seating arrangement?

Explanation / Answer

a) One pivot is fixed - (n-1)!

b) Number of seating arrangements = n ! ( Linear permutations since one chair is throne)

c) Number of seating arrangement = n-1! ( Circular permutations)

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