- #1
annpaulveal
- 15
- 0
Homework Statement
In how many ways can a group of 9 women and 6 men be seated at a circular table if no two men can be seated next to each other?
Homework Equations
The Attempt at a Solution
I have come up with a solution, but I'm unsure if my reasoning is correct...
First, I started with the 9 women. They can be arranged in 8! ways / 9 rotations = 4480 options.
Then, I drew a picture of a 12-person table, placing a man between each woman. This is where I think I may have done something wrong. The men can be placed in 5! ways, divided by 12 for rotations = 10 options.
Finally, I drew a picture of the 15-person table. The three remaining women can be placed in 36 different places, with three possibilities existing between each female/male pair. This can be calculated as 36 choose 3, divided by 15 rotations = 476 options.
The final answer would be all three options multiplied together, so 4480(10)(476).
As I said, I have a feeling that I did something wrong, so I would really appreciate some suggestions to get me back on track :)