document.write( "Question 1147711: Please help me solve: A committee consisting of 3 faculty members and 5 students is to be formed. Every committee position has the same duties and voting rights. There are 11 faculty members and 13 students eligible to serve on the committee. In how many ways can the committee be formed? \n" ); document.write( "

Algebra.Com's Answer #769069 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Since the problem says that \"every committee position has the same duties and voting rights\",\r\n" );
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document.write( "it means that the order does nor matter in this problem;  hence, the problem is about COMBINATIONS and not about permutations.\r\n" );
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document.write( "3 faculty members from 11 faculty members can be selected by   =  = 165 ways.\r\n" );
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document.write( "5 students from 13 students can be selected by   =  = 1287 ways.\r\n" );
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document.write( "Since these selections among faculty members and students are independent, the total number of ways is the product\r\n" );
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document.write( "    . = 165*1287 = 212355.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "On Combinations, see introductory 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( "\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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