document.write( "Question 1067586: 25 books are placed at random in a book shelf.
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Algebra.Com's Answer #682727 by Edwin McCravy(20056) $\"\"$ $\"About$

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25 books are placed at random in a book shelf.
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document.write( "Always together:\r\n" );
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document.write( "Successful arrangements:\r\n" );
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document.write( "Imagine tying a string around the three particular books, and \r\n" );
document.write( "considering that package as a single \"thing\". Then there are \r\n" );
document.write( "only 23 \"things\" to arrange, 22 non-particular books and 1 \r\n" );
document.write( "group of the three particular books tied together.  There are \r\n" );
document.write( "3! ways to arrange the 3 particular books before tying them \r\n" );
document.write( "together, and for each of those, there are 23! ways to arrange \r\n" );
document.write( "the 23 \"things\".\r\n" );
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document.write( "The number of successful arrangements is (3!)(23!)\r\n" );
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document.write( "The number of possible arrangements is 25!\r\n" );
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document.write( "Probability = [(3!)(23!)]/(25!) = 1/100\r\n" );
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document.write( "Never together \r\n" );
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document.write( "Successful arrangements:\r\n" );
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document.write( "Think of first putting the 22 non-particular book on\r\n" );
document.write( "the shelf, and then inserting the three particular books\r\n" );
document.write( "among them so that no two are together.\r\n" );
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document.write( "For each of the 22! arrangements of the 22 non-particular\r\n" );
document.write( "books on the shelf there are 23 places to put the three\r\n" );
document.write( "particular books.  To explain, these 23 places are:\r\n" );
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document.write( " 1. on the far left, (left of the 1st non-particular book)\r\n" );
document.write( " 2. between the 1st and 2nd non-particular books\r\n" );
document.write( " 3. between the 2nd and 3rd non-particular books\r\n" );
document.write( " 4. between the 3rd and 4th non-particular books\r\n" );
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document.write( "20. between the 19th and 20th non-particular books\r\n" );
document.write( "21. between the 20th and 21st non-particular books\r\n" );
document.write( "22. between the 21st and 22nd non-particular books\r\n" );
document.write( "23. on the far right, (right of the 22nd non-particular book)\r\n" );
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document.write( "Number the 3 particular books first, second and third.\r\n" );
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document.write( "There are 23 places to put the first particular book.\r\n" );
document.write( "There are then 22 places to put the second particular book.\r\n" );
document.write( "There are then 21 places to put the third particular book.\r\n" );
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document.write( "The number of successful arrangements is (22!)(23)(22)(21)\r\n" );
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document.write( "The number of possible arrangements is 25!\r\n" );
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document.write( "Probability = (22!)(23)(22)(21)/(25!) = 77/100\r\n" );
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document.write( "Edwin

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