+62 It is a beautiful day at the beach and ten beach volleyball players have shown up at the volleyball courts. Each two-person volleyball team should consist of a setter and a spiker. Five of the players prefer to be a spiker, four of the players prefer to be a setter, and one player is fine either way.
In how many ways can a two-person team be assembled such that no player feels out of position?
+506 There are 2 cases: one case where the player who is fine either way is not in the two-person team, or another case where that player is.
For case 1, there are \(5\cdot4=20\) ways to select the teams, since there are 5 possibilities for a spiker and 4 for a setter.
For case 2, there are 9 ways to select the team, since the player who is fine either way can pair up with any of one of the 9 remaining people.
In total, there are \(20+9=\boxed{29}\) ways.
