document.write( "Question 1208392: On a library shelf there are 5 different science books and 4 different math books. Find the number of ways to arrange the books next to each other on the shelf in the following cases: No two math books are next to each other. \n" ); document.write( "

Algebra.Com's Answer #846791 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "On a library shelf there are 5 different science books and 4 different math books.
\n" ); document.write( "Find the number of ways to arrange the books next to each other on the shelf
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document.write( "With 5 Science book on the bookshelf, we have 4 + 1 + 1 = 6 possible positions for the Math books\r\n" );
document.write( "(4 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 4 different Math books is  \r\n" );
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document.write( "     =  = 3*5 = 15.\r\n" );
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document.write( "We should multiply it by  5! = 120 (the number of permutations of 5 Science books)\r\n" );
document.write( "and by 4! = 24 (the number of permutations of 4 Math books).\r\n" );
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document.write( "So, the final answer is  15*120*24 = 43200.\r\n" );
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