document.write( "Question 1103356: 6 freshmen, 8 sophomores, 10 juniors, and 9 seniors are eligible to be on a committee. If a committee of 14 students is chosen at random, what is the probability that it is made up of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors? \r
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Algebra.Com's Answer #718044 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let me solve  MORE SIMPLE  problem for you.\r\n" );
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document.write( "     6 freshmen  and  8 sophomores are eligible to be on a committee. \r\n" );
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document.write( "     If a committee of 5 students is chosen at random, what is the probability that it is made up of 3 freshmen and 2 sophomores? \r\n" );
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document.write( "In all, there are 6 + 8 = 14 students to choose from.\r\n" );
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document.write( "So, there are \"C%5B14%5D%5E5\" ways to made the committee of 5 students. \r\n" );
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document.write( "It is your  TOTAL space  of events,  and it has  \"%2814%2A13%2A12%2A11%2A10%29%2F%281%2A2%2A3%2A4%2A5%29\" = 2002 elements in all.\r\n" );
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document.write( "Next, in how many ways can you choose 3 freshmen   of 6 ?   - In \"C%5B6%5D%5E3\" = \"%286%2A5%2A4%29%2F%281%2A2%2A3%29\" = 20 ways.\r\n" );
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document.write( "      In how many ways can you choose 2 sophomores of 8 ?   - In \"C%5B8%5D%5E2\" = \"%288%2A7%29%2F%281%2A2%29\" = 28 ways.\r\n" );
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document.write( "Thus   there are \"C%5B6%5D%5E3\".\"C%5B8%5D%5E2\" = 20*28 = 560 ways to form the committee in accordance with the given requirements.\r\n" );
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document.write( "So, the probability under the question is  P = \"560%2F2002\".\r\n" );
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document.write( "Or, if you want to have it as a \"formula\",  P = \"%28C%5B6%5D%5E3%2AC%5B8%5D%5E2%29%2FC%5B6%2B8%5D%5E%283%2B2%29\".\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
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\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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\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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