document.write( "Question 1173252: mr. santos has set 8 questions for a math test.\r
\n" ); document.write( "\n" ); document.write( "c.) if the most difficult question and the easiest one are set next to each other, how many permutations are there for the 8 questions?\r
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Algebra.Com's Answer #798460 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "8 items have 8! = 8*7*6*5*4*3*2*1 = 40320  permutations.\r\n" );
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document.write( "But in this problem, we consider not all the permutations.\r\n" );
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document.write( "We consider only THOSE, where the most difficult question and easiest question are set next to each other.\r\n" );
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document.write( "So, these two questions always are neighbor.\r\n" );
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document.write( "It means, that we consider these two objects as two clued together;\r\n" );
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document.write( "so we actually consider 7 objects, and this special object can exist in two states (ED) or (DE), depending\r\n" );
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document.write( "which one of the two questions, easy (E) or difficult (D), goes first.\r\n" );
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document.write( "THEREFORE, the total number of all such possible permutations is \r\n" );
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document.write( "    2*7! = 2 * (7*6*5*4*3*2*1) = 2 * 5040 = 10080.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to see many similar solved problems on PERMUTATIONS, see my lessons\r
\n" ); document.write( "\n" ); document.write( "    - Introduction to Permutations\r
\n" ); document.write( "\n" ); document.write( "    - PROOF of the formula on the number of Permutations\r
\n" ); document.write( "\n" ); document.write( "    - Simple and simplest problems on permutations\r
\n" ); document.write( "\n" ); document.write( "    - Special type permutations problems \r
\n" ); document.write( "\n" ); document.write( "    - Problems on Permutations with restrictions \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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