document.write( "Question 1125217: A bag contains three 20-dollar bills, three 10-dollar bills, and three 5-dollar bills. Three bills are selected from the bag at random. Let the random variable X represent the total dollar value of the selected bills. \r
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\n" ); document.write( "\n" ); document.write( "What is the least possible value of X?
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\n" ); document.write( "\n" ); document.write( "What is the greatest possible value of X?
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\n" ); document.write( "\n" ); document.write( "What is Pr(X=30)?
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\n" ); document.write( "\n" ); document.write( "Enter your answers as whole numbers or fractions in lowest terms. Your answers should all be numeric -- do not use dollar signs in your answers. \n" ); document.write( "
Algebra.Com's Answer #741629 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "            The solution by the tutor @math-helper is fine.\r
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\n" ); document.write( "\n" ); document.write( "            I want to show you different way to solve the last part.\r
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document.write( "There are two ways to get 30:  30 = 10+10+10   and/or   30 = 20 + 5 + 5.\r\n" );
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document.write( "There are no other ways.\r\n" );
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document.write( "In all, there are  \"C%5B9%5D%5E3\" = \"%289%2A8%2A7%29%2F%281%2A2%2A3%29\" = 84 different groups of three banknotes (without looking the order).\r\n" );
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document.write( "Of these 84 groups, there is only one group containing 3 \"tens\". It contributes  \"1%2F84\" to the total probability.\r\n" );
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document.write( "Also, there are 9 groups containing (20,5,5) in any order.   \r\n" );
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document.write( "                                    (9 = 3 ways to get 20 from the 3 \"T\"  MULTIPLIED  by 3 ways to get the pair (5,5)  from 3 \"F\").\r\n" );
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document.write( "                                                                 It contributes  \"9%2F84\" to the total probability.\r\n" );
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document.write( "So, the total probability under the question for this part of the problem is  \"1%2F84\" + \"9%2F84\" = \"10%2F84\" = \"5%2F42\",\r\n" );
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document.write( "which coincides with the answer by the tutor @math-helper.\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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