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 #846796 by Edwin McCravy(20056)\"\" \"About 
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document.write( "First we'll arrange the books only subject-wise, as if the math books were\r\n" );
document.write( "indistinguishable and the science books were also indistinguishable. Then we'll\r\n" );
document.write( "rearrange (permute) them.  \r\n" );
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document.write( "We start out with this configuration of all 5 math books with only 3 of the\r\n" );
document.write( "science books separating them.\r\n" );
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document.write( "   _ M S M S M S M _\r\n" );
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document.write( "I have underlined the 5 places we can put the other two science books. Each of\r\n" );
document.write( "the three underlined S indicates that you can put one or both of them in with that\r\n" );
document.write( "S, since science books can be placed together.  The 2 empty underlines indicate\r\n" );
document.write( "places where they can go as well, left or right of the others.\r\n" );
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document.write( "Case 1. You imagine \"gluing\" the 2 science books together and inserting the\r\n" );
document.write( "\"glued pair\" in one of those 5 underlined places. That's 5 ways.\r\n" );
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document.write( "Case 2.  You pick 2 separate underlined places to put them separately in. That's\r\n" );
document.write( "C(5,2)=10 more ways.\r\n" );
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document.write( "So altogether, there would be only 5+10=15 ways to arrange them if the math\r\n" );
document.write( "books were indistinguishable, and the science books were also indistinguishable.\r\n" );
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document.write( "But since none are indistinguishable books, we multiply by 5! to permute the\r\n" );
document.write( "science books and by 4! to permute the math books.\r\n" );
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document.write( "Answer (15)(5!)(4!) = (15)(120)(24) = 43200 ways.\r\n" );
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document.write( "Edwin
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