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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?

 Jan 18, 2022
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My take on this is that if the one player that is fine either way is a spiker, there are 6*4 =24 possible teams from that. We have to add 5 more teams if the player is a setter instead of 5*5=25, since we would be overcounting the times when the player is not included.

So there are 24+5=29 teams that can be assembled.

 Jan 18, 2022

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