So here's the question:
In how many ways can 5 women and 5 men be arranged at a circular table if three people insist on sitting together?
"Circular Permutation Principle, n different objects can be arranged in a circle in (n-1)! ways."
My thoughts: Since three people insist on sitting together, that gives us 10 - 3 = 7 people. So it should be (7-1)! * 'something'. The something I can't figure out. Since the three people can sit in different orders. Is it 3! something = 3!
I don't know if I'm right or not.
Choose one of the people not in the special group. Fix this person at chair 0.
The 3 people who must be together can be treated as 1 person. This means you have essentially 8 people. Since one person is fixed at chair 0, that leaves 7! ways to arrange them. The 3 people can themselves be arranged in 3! ways. So I get 3! x 7! ways. Agree? Disagree?