document.write( "Question 1172654: Taking an algorithm course and working a union-find problem. Algebra & trig too long ago (high school in 1970s) to remember how to calculate permutations. If I have N objects how many union operations do I need for each object to paired with every other object in the set? I looked at permutation and combination formulas and do not understand the ! symbol. \n" ); document.write( "
Algebra.Com's Answer #797741 by ikleyn(52790)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "From your post, I do not understand clearly the exact meaning of the problem.\r\n" );
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document.write( "So, I only can/may guess.\r\n" );
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document.write( "If you need to find the number of pairs, which you can create using n objects,\r\n" );
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document.write( "then the answers are as follow:\r\n" );
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document.write( "    a)  if we combine different objects in pairs and if the order is important,\r\n" );
document.write( "        then the number of pairs is N*(N-1)    (permutations).\r\n" );
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document.write( "    b)  if we combine different objects in pairs and if the order is NOT important,\r\n" );
document.write( "        then the number of pairs is \"%28N%2A%28N-1%29%2F2%29\"    (combinations).\r\n" );
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\n" ); document.write( "\n" ); document.write( "For introductory lessons on permutations and combinations, see\r
\n" ); document.write( "\n" ); document.write( "    - Introduction to Permutations\r
\n" ); document.write( "\n" ); document.write( "    - PROOF of the formula on the number of Permutations\r
\n" ); document.write( "\n" ); document.write( "    - Simple and simplest problems on permutations\r
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\n" ); document.write( "\n" ); document.write( "    - Introduction to Combinations\r
\n" ); document.write( "\n" ); document.write( "    - PROOF of the formula on the number of Combinations\r
\n" ); document.write( "\n" ); document.write( "    - Problems on Combinations\r
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\n" ); document.write( "\n" ); document.write( "    - Miscellaneous problems on permutations, combinations and other combinatoric entities \r
\n" ); document.write( "\n" ); document.write( "    - Fundamental counting principle problems \r
\n" ); document.write( "\n" ); document.write( "    - Nice recreational problems on permutations \r
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\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on Permutations and Combinations\r
\n" ); document.write( "\n" ); document.write( "in this site.   //   I listed here the \"introductory\" lessons only . . . \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
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\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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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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