Will mark 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.