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Ten friends decide to play a game, five against five. There are
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document.write( "There are 2 triplets and 4 \"single\" friends.\r\n" );
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document.write( "We cannot choose both triplets for the same team since there can \r\n" );
document.write( "only by 5 on a team. \r\n" );
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document.write( "We only need to choose one team, for the ones that are left\r\n" );
document.write( "will automatically make up the other team.\r\n" );
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document.write( "We choose one of the triplets. Then there are the combinations\r\n" );
document.write( "of 4 single friends taken 2 at a time to go with that triplet.\r\n" );
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document.write( "The answer is C(4,2) = 6 ways\r\n" );
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document.write( "[Don't make the mistake of thinking there are 2 choices for the triplets,\r\n" );
document.write( "since we only need to pick one triplet and assign two of the 4 \"single\"\r\n" );
document.write( "players to be with that triplet, since the other team with the other \r\n" );
document.write( "triplet will automatically be chosen once we choose the 2 to go with that \r\n" );
document.write( "one triplet.]\r\n" );
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document.write( "Suppose one triplet is {A,B,C}, the other triplet (D,E,F}, and the\r\n" );
document.write( "four \"single\" people are {G,H,I,J}\r\n" );
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document.write( "All 6 ways to divide the teams are:\r\n" );
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document.write( "1. {A,B,C,G,H} and the other team {D,E,F,I,J}\r\n" );
document.write( "2. {A,B,C,G,I} and the other team {D,E,F,H,J}\r\n" );
document.write( "3. {A,B,C,G,J} and the other team {D,E,F,H,I}\r\n" );
document.write( "4. {A,B,C,H,I} and the other team {D,E,F,G,J}\r\n" );
document.write( "5. {A,B,C,H,J} and the other team {D,E,F,G,I}\r\n" );
document.write( "6. {A,B,C,I,J} and the other team {D,E,F,G,H}\r\n" );
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document.write( "Edwin\r\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "