document.write( "Question 1126530: A woman has 11 friends and she would like to invite 5 of them for a get together, in how many ways can this be done if 2 of her 11 friends are not on speaking terms and will not attend together? \n" ); document.write( "
Algebra.Com's Answer #742884 by ikleyn(52787)\"\" \"About 
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document.write( "In all, there are  \"C%5B11%5D%5E5\" = \"%2811%2A10%2A9%2A8%2A7%29%2F%281%2A2%2A3%2A4%2A5%29\" = 462 ways to form group of 5 from 11 items (persons).\r\n" );
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document.write( "Of them, those groups are prohibited (and must be subtracted from 462) that contain these two special friends.\r\n" );
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document.write( "So we need to count the number of such groups.\r\n" );
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document.write( "The number of such groups is exactly the number of ways you can complement these two special persons to the group of 5, \r\n" );
document.write( "by adding 3 other persons from 11-2 = 9 remaining.\r\n" );
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document.write( "You can do it in   \"C%5B9%5D%5E3\" = \"%289%2A8%2A7%29%2F%281%2A2%2A3%29\" = 84 ways.\r\n" );
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document.write( "So, the answer to the problem question is this difference\r\n" );
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document.write( "    462 - 84 = 378.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On Combinations,  see the lessons\r
\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
\n" ); document.write( "\n" ); document.write( "    - OVERVIEW of lessons on Permutations and Combinations\r
\n" ); document.write( "\n" ); document.write( "in this site.\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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