document.write( "Question 1100362: In a basketball game competition, there are many teams and each team plays with each other once. Find the total number of matches played if there are 3 teams? \n" ); document.write( "

Algebra.Com's Answer #714835 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "If \"n\" teams play each with other and only once, then the total number of matches is .\r\n" );
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document.write( "It is easy to understand:  each team plays with (n-1) others.\r\n" );
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document.write( "So, it looks like there are n(n-1) matches in all.\r\n" );
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document.write( "But counting in this way, we count each match twice, for one and for other team.\r\n" );
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document.write( "Therefore, we must divide n*(n-1) by 2 to get the correct answer.  \r\n" );
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document.write( "For 3 teams the answer is  = 3,\r\n" );
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document.write( "and the list of matches (combinations of the team A, B and C) is THIS:\r\n" );
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document.write( "(A,B), (A,C) and (B,C).\r\n" );
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\n" ); document.write( "There are other similar problems of this kind:\r
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document.write( "    - the number of handshakes between \"n\" people;\r\n" );
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document.write( "    - the number of diagonals of n-sided polygon;\r\n" );
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document.write( "    - the number of straight lines in a plane, connecting \"n\" given points\r\n" );
document.write( "          placed in a way that NO 3 points lie in one straight line.\r\n" );
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