document.write( "Question 1189221: A committee of six is to be chosen from the 20 members of the student council. In how many ways can this be done if:\r
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\n" ); document.write( "\n" ); document.write( "B. There are twelve junior members and 8 senior members and the committee must include 2 junior and four senior members?\r
\n" ); document.write( "\n" ); document.write( "C. There must be at least 2 senior members on the committee. ( I need help with this one in particular)\r
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Algebra.Com's Answer #820528 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "A committee of six is to be chosen from the 20 members of the student council.
\n" ); document.write( "In how many ways can this be done if:
\n" ); document.write( "A. There are no restrictions.
\n" ); document.write( "B. There are twelve junior members and 8 senior members and the committee must include 2 junior and four senior members?
\n" ); document.write( "C. There must be at least 2 senior members on the committee. ( I need help with this one in particular)
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\n" ); document.write( "\n" ); document.write( "            As you request,  I solve the problem's  Part  C   only.\r
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document.write( "\"at least 2 senior members\" means 2, or 3, or 4, or 5, or 6 senior members.\r\n" );
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document.write( "So, the formula is\r\n" );
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document.write( "    in how many ways =  = \r\n" );
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document.write( "                     = 28*495 + 56*220 + 70*66 + 56*12 + 28*1 = 31500 ways.    ANSWER\r\n" );
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Post-solution notes

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\n" ); document.write( "\n" ); document.write( "        (1)   The formula is self-explanatory . . . \r
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\n" ); document.write( "\n" ); document.write( "        (2)   It is tedious to calculate the binomial coefficients  (combinations)  manually - - - \r
\n" ); document.write( "\n" ); document.write( "                - - - so I used the  Excel standard function  combin(n,k)  as a calculator.\r
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\n" ); document.write( "\n" ); document.write( "To make your horizon wider and the ground under your legs solder,  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( "    - Problems on Combinations with restrictions \r
\n" ); document.write( "\n" ); document.write( "    - Fundamental counting principle problems \r
\n" ); document.write( "\n" ); document.write( "    - Some twisted combinatorics problem \r
\n" ); document.write( "\n" ); document.write( "    - Math circle level problem 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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