document.write( "Question 1099187: Ten persons gather for a meeting. Before the meeting begins, each person shakes hands with every other person exactly once. How many handshakes are there altogether?
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Algebra.Com's Answer #713610 by ikleyn(52790)\"\" \"About 
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document.write( "One handshake is a \"combination\" of two persons.\r\n" );
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document.write( "The term \"combination\" is used here in its mathematical meaning as it is used in Combinatorics.\r\n" );
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document.write( "Therefore, the total number of handshakes is equal to the total number of combinations of 10 people taken 2 at a time:\r\n" );
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document.write( "\"C%5B10%5D%5E2\" = \"%2810%2A9%29%2F2\" = \"90%2F2\" = 45.\r\n" );
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document.write( "In the general case of n people the formula for the number of handshakes is  \"C%5Bn%5D%5E2\" = \"%28n%2A%28n-1%29%29%2F2\".\r\n" );
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\n" ); document.write( "On Combinations, see the lessons\r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic  \"Combinatorics: Combinations and permutations\". \r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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