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Social ScienceQuestion # 4 Consider a circular table with N > 4 seats. Chris and Sarah are two of Nth at ests to be seated at this table. In how many ways can the dinner guests be seateda) Chris and Sarah are not adjacent.b) Chris and Sarah are adjacent.
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Question # 4 Consider a circular table with N > 4 seats. Chris and Sarah are two of N th at ests to be seated at this table. In how many ways can the dinner guests be seated a) Chris and Sarah are not adjacent. b) Chris and Sarah are adjacent.
Expert Answer
Given a circular table with N seats (N ≥4). Chris and Sarah are two among the N dinner guests,
Let us suppose there are N seats around table.
Other than Chris and Sarah, there are N-2 guests. Keeping Sarah a side we have N-1 guests.
The number of ways of seating arrangment of N poeple across a round table is (N-1)! ways.
So from the given case number of different ways of seating of N-1 guests around a round table is (N-1-1)! = (N-2)!
So now N-1 guests excluding Sarah are arranged in a round table in (N-2)! ways. Now we need Chris and Sarah not to be adjacent. So the remainig one chair of Sarah can be placed such that it is not adjacent to Chris.
N-1 seats will have N-1 spots between them and we canno...
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