document.write( "Question 948073: There are 13 indistinguishable math books and 5 indistinguishable physics books
\n" ); document.write( "that are to be placed on a bookshelf so that between any two physics books there
\n" ); document.write( "must be at least 2 math books. In how many different ways this can be done \n" ); document.write( "
Algebra.Com's Answer #579929 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Start by putting the arrangement of books below on the \r\n" );
document.write( "shelf so that there are exactly 2 math books between any \r\n" );
document.write( "two physics books there.\r\n" );
document.write( "\r\n" );
document.write( "     __PMM__PMM__PMM__PMM__MP__\r\n" );
document.write( "\r\n" );
document.write( "(M stands for a math book and P for a physics book, and the 6 blanks\r\n" );
document.write( "are gaps or places where we can insert the remaining math books\r\n" );
document.write( "\r\n" );
document.write( "All 5 physics books, P's, and 8 of the 13 math books, M's are on the \r\n" );
document.write( "shelf.  So we have to insert the remaining 5 math books, M's, into\r\n" );
document.write( "some of the 6 blanks.   \r\n" );
document.write( "\r\n" );
document.write( "That's the number of partitions of 5 things into 6 blanks,\r\n" );
document.write( "(which includes putting no M's in some or even \r\n" );
document.write( "all but 1 space, and all 5 in that space.)\r\n" );
document.write( "\r\n" );
document.write( "The number of partitions of n indistinguishable things into r places. \r\n" );
document.write( "[which includes putting 0 in some places, and extreme cases where all n\r\n" );
document.write( "things are in 1 place.]\r\n" );
document.write( "\r\n" );
document.write( "is \r\n" );
document.write( "\r\n" );
document.write( "(n+r-1)C(r-1), where n=5, r=6\r\n" );
document.write( "\r\n" );
document.write( "(5+6-1)C(6-1) = 10C5 = 252 ways to arrange the books.\r\n" );
document.write( "\r\n" );
document.write( "Answer: 252\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );