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# It is a beautiful day at the beach and ten beach volleyball players have shown up at the volleyball courts. Each two-person

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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?

Oct 8, 2018

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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

Oct 8, 2018
edited by CPhill  Oct 8, 2018