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?

Firewolf Oct 8, 2018

#1**+1 **

Here's my attempt at this

If the one player wants to be a spiker we can choose any 1 of 6 people to be a spiker and any 1 of 4 people to be a setter ....so

C(6,1) * C(4,1) = 6 * 4 = 24 possible teams

If the one player wants to be a setter, we can choose 1 of 5 people to be setters and 1 of 5 people to be spikers...so

C(5,1) * C(5,1) = 5 * 5 = 25 possible teams

So....the total number of different teams = 24 + 25 = 49

CPhill Oct 8, 2018