document.write( "Question 1089768: In how many ways can a committee consisting of 2 faculty members and 5 students be formed if there are only 11 faculty members and 12 students eligible to serve on the committee? \n" ); document.write( "
Algebra.Com's Answer #704158 by ikleyn(52834)\"\" \"About 
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document.write( "1.  In how many ways can you select 2 members among 11 faculty members?\r\n" );
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document.write( "    Since the order is not important, there are \"C%5B11%5D%5E2\" = \"%2811%2A10%29%2F2\" = 55 ways.\r\n" );
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document.write( "2.  In how many ways can you select 5 students among 12 students?\r\n" );
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document.write( "    Since the order is not important, there are \"C%5B12%5D%5E5\" = \"%2812%2A11%2A10%2A9%2A8%29%2F%281%2A2%2A3%2A4%2A5%29\" = 792 ways.\r\n" );
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document.write( "3.  Now, the selections among these two groups are independent.\r\n" );
document.write( "    Hence, in all , you have 55*792 ways in your global problem.\r\n" );
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\n" ); document.write( "\n" ); document.write( "These magic numbers  \"C%5Bn%5D%5Ek\"  are called the numbers of combinations of  n  things taken  k  at a time.\r
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\n" ); document.write( "\n" ); document.write( "About combinations and about these numbers, 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
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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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