document.write( "Question 732291: Ten students are in pairs on a field trip. How many different pairs of students are possible? \n" ); document.write( "

Algebra.Com's Answer #852916 by ikleyn(53418) $\"\"$ $\"About$

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\n" ); document.write( "Ten students are in pairs on a field trip.
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\n" ); document.write( "\n" ); document.write( " $\"%2810%2A9%29%2F2\"$ = $\"90%2F2\"$ = 45 different ways to make pairs of 10 students are possible.\r
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\n" ); document.write( "\n" ); document.write( "It is the number of combinations of 10 items taken 2 at a time.\r
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\n" ); document.write( "\n" ); document.write( "The order in pairs does not matter, so we use combinations.\r
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document.write( "    To better understand the problem, imagine 10 x 10 grid on graph paper.\r\n" );
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document.write( "    Each point in this grid represent one pair.\r\n" );
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document.write( "    The diagonal (10 points) should be excluded: 100 minus 10 gives 90,  100-10 = 90.\r\n" );
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document.write( "    The pints symmetric about the diagonal, represent the same pair.\r\n" );
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document.write( "    So, we divide 90 by 2 and get the same 45 what we need.\r\n" );
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document.write( "    It is the geometric interpretation for your better understanding.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "The answer in the post by @lynnlo is incorrect. \r
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\n" ); document.write( "\n" ); document.write( "Simply ignore his post.\r
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