11 players of Team A and 11 players of Team B sit at a round table, the players from the two teams alternate, the goalkeepers sit together, but the captains do not sit together. In how many different ways can they be seated?
Here is my attempt. assume the goalkeepers are sitting on the same chair (since they must be sitting together). There are 20 spots for them. If one of the captain is sitting next to the goalkeeper,(either left or right side, either from team A or team B) there are 2*2*9 ways for the other captain to sit. If captains are not sitting next to the goalkeepers, there are (8*8-(22-6-1)) ways. and the rest of the players have (8!*8!) ways. So totally 2*2*9*(8*8-(22-6-1))*(8!*8!) ways.