document.write( "Question 1208407: On a library shelf there are 7 different science books and 5 different math books.
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Algebra.Com's Answer #846805 by ikleyn(52777) $\"\"$ $\"About$

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\n" ); document.write( "On a library shelf there are 7 different science books and 5 different math books.
\n" ); document.write( "Find the number of ways to arrange the books next to each other on the shelf
\n" ); document.write( "if no two math books are next to each other.
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document.write( "With 7 Science book on the bookshelf, we have 6 + 1 + 1 = 8 possible positions for the Math books\r\n" );
document.write( "(6 positions between the Science books, one position on the left and one position on the right).\r\n" );
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document.write( "So, the number of all different placements of 5 different Math books is  \r\n" );
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document.write( "     =  = 8*7 = 56.\r\n" );
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document.write( "We should multiply it by  7! = 1*2*3*4*5*6*7 = 5040 (the number of permutations of 7 Science books)\r\n" );
document.write( "and by 5! = 120 (the number of permutations of 4 Math books).\r\n" );
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document.write( "So, the final answer is  56*5040*120 = 33,868,800.\r\n" );
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\n" ); document.write( "\n" ); document.write( "This problem is a TWIN to the other similar problem which I solved here at the forum yesterday under this link\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Permutations/Permutations.faq.question.1208392.html\r
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