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?
If we choose the one who is fine either way to be a spiker....we have to choose one of 6 spikers and one of 4 setters = 6 * 4 = 24 ways
If we choose the one who is fine either way to be a setter we have to choose one of 5 spikers and one of 5 setters = 5 * 5 = 25 ways
So 25 + 24 = 49 ways