"Six men and 6 females are to be seated around a circular table. Every person must be sitting opposite of another person of the same sex. How many different seatings are possible?" * Ok here's my logic, If you have 12 people, and just want to seat them, you can do so in 11! ways... * So if you sit 3 men anywhere, then opposite you can sit the rest of the men... I think this would be like P(12 3)... * Then you just seat the women in the rest of the seats; 5! ways... So total ways, would be something along the lines of P(12 3) + 5!. I don't think that's right, so that's why I'm here asking for help.