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Asked Feb 12, 2019
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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.
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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.

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Expert Answer

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. 

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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)! 

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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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Basic Probability

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