Question

Asked Feb 12, 2019

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Step 1

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.

Step 2

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)!

Step 3

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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