document.write( "Question 1192101: In a volleyball game, each team must play with all the other teams. How many games will there be? \n" ); document.write( "

Algebra.Com's Answer #824001 by math_helper(2461) $\"\"$ $\"About$

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document.write( "You didn't specify how many teams there are, and the answer depends on the number of teams, N.\r
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document.write( "Looking at TOTAL games played here, by all teams:\r
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document.write( "For N = 2, obviously 1 game will be played
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document.write( "For N = 3, there will be 3 games (A,B,C:  unique games: A plays B, B plays C, A plays C)
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document.write( "For N = 4, there will be 6 games  (A,B,C,D: unique games: A plays B,C,D; B plays C,D, C plays D)\r
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document.write( "...  For the general case, there are   games played in TOTAL.\r
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document.write( "[ While each INDIVIDUAL team plays N-1 games, there is overcounting if we just multiply N-1 by N.  See for example the N=4 case where I omitted \"B plays A\" because that is already counted in \"A plays B\".  Hope this makes sense. ] 
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