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A committee with nine people gather to have a meeting. The members sit around a circular table. Two of the committee members, Rick and Morty, want to sit so that there is exactly one person between them. How many different seatings are possible? (Two seatings are considered the same if one can be rotated to obtain the other.)

 Jan 8, 2020
 #1
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The number of possible seatings is 9!*2*2/9 = 161280.

 Jan 8, 2020
 #2
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Anchor  Rick and Morty in any two seats

 

And they can be arranged in 2 ways

 

And we have  C(7,1)  =  7  ways to pick  the person  to sit between them

 

And the other members can be arranged in 6! ways  = 720 ways

 

So......the total arrangements   =

 

2 * 7  * 720   = 

 

10080  possible seatings 

 

 

cool cool cool

 Jan 8, 2020

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