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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?

 Mar 1, 2022
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The one that is not choosy is going to be a Setter.  That way there are 5 setters  and 5 spikers 

 

Take a setter, makes no difference which one.  She can be matched with any of 5 spikers

Take another setter.  She can be matched with any of the remaining 4 spikers.

etc

So the answer will be   5! = 120 ways

 Mar 2, 2022
edited by Melody  Mar 2, 2022

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