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8. The Last Supper
On the last night of Scout camp, Chris, his wife Jo and the 11 other adults sit down for
supper along one side of a long rectangular table.
Chris takes the central seat, with six adults on each side of him.
Jo must sit next to Chris.
Alex, Barb and Dave insist on being next to one another (in any order) on the side to
Chris's left.
Eddie, Fred and Gareth are fed up with Alex's snoring, so they refuse to be on the same
side of Chris as him.
Heather, Iris, Kane, Luke and Michael have no seating preferences.
How many arrangements of the adults are possible?

Answer :

MrRoyal

The number of possible seats is an illustration of permutation

There are 1728 possible sitting arrangements

How to determine the number of seats

From the question, we have the following highlights:

  • Chris can only take 1 seat (i.e. the central seat)
  • Jo can take 2 seats (i.e. the seats adjacent the central seat)
  • Alex, Barb and Dave can take 3! number of seats
  • Eddie, Fred, and Gareth can take 3! number of seats on the right of Chris.
  • The remaining 4 adults do not have preference, then they can seat in 4! ways

So, the number of sitting arrangement is:

[tex]n = 1 * 2 * 3! * 3! * 4![/tex]

Evaluate the product

[tex]n = 1728[/tex]

Hence, there are 1728 possible sitting arrangements

Read more about permutation at:

brainly.com/question/12468032

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