elrond is organizing a council in rivendell. he has invited two men, two dwarves, and two elves, and plans to seat them along with himself in a circle with seven seats. he knows that dwarves and elves do not get along, so he plans to seat them so that no dwarf is sitting next to an elf. the circle has a head chair. if elrond (himself an elf) must sit at the head of the circle, in how many ways can he seat the other six guests? all beings are distinguishable from one another, and the head chair is distinguishable from the other chairs.

A cycle is a shape made up of all the points in a rectangle that are a certain distance from the center. It is the curve drawn by a moving location in a rectangle so that the radius from a given stage remains constant.

The radius of a circle is the distance between any two locations on the circle and the canter.

In most cases, the radius must be positive. A circle with r=0 is a degenerate instance. This section is about rounds in Euclidean geometry, primarily the Euclidean plane, unless otherwise noted.

Now we have to consider the conditions:

Elrond is holding a council at Rivendell. He's invited two men, two dwarves, and two elves, and plans to seat them all in a circle with seven seats, including himself. so 5+6=11

He understands that dwarves and elves do not get along, therefore he plans to arrange them so that no dwarf seats next to an elf. In the center of the circle is a chair. Hence 2=2 = 4

Number of ways = 11+4 = 15

Therefore Elrond can sit his guest in 15 ways around the circle such that all conditions are fulfilled.

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