Suppose the nine players are A,B,C,D,E,F,G,H,I Suppose A and B cannot be on the same team. There are two cases. Case 1. Neither A nor B is the umpire. A is on one team and B is on the other. Then we choose the umpire from the 7 players C,D,E,F,G,H,I. That's 7 ways to pick the umpire. We have 6 players left. We choose 3 to play on the team with A in 6C3 = 20 ways, and the remaining 3 will play on the team with B in 3C3 = 1 way. That's 7∙20∙1 = 140 ways for case 1. Case 2. A or B is the umpire. We choose the umpire 2 ways. Then we have 8 players choose 4 on one team in 8C4 = 70 ways, and that leaves 4C4 = 1 way to put the others on the other team. That's 2∙70 = 140 ways for case 2. So that's 140 for case 1 and 140 for case 2, a total of 280 ways. Edwin