document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1107161>Question 1107161</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 4 different mathematics bookd and 5 different science books. In how many ways can the books be arranged on a shelf if<BR>\n" );
document.write( "A. There are no restrictions<BR>\n" );
document.write( "B. Books of the same subject must be placement together<BR>\n" );
document.write( "C. If they must be placed alternately </SPAN>\n" );
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document.write( "A.  There are 9 distinguishable items (books), so they can be arranged in 9! ways.  (9 choices for the first book, times 8 for the 2nd book, …, times 2 for the 8th book, times 1 for the 9th book).   <BR>\n" );
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document.write( "B.  Keeping the same subjects together, there are 4! ways to arrange the mathematics books, and 5! ways to arrange the science books.  Additionally, you can have the groups themselves arranged two ways (one with math on the left, the other with math books on the right):  4!*5!*2 <BR>\n" );
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document.write( "C.  For this arrangement, the science books need to be on the ends (S-M-S-M-S-M-S-M-S) in order to 'sandwich' the math books.    There are 5 places to hold science books and 4 places for math books, so I'd say 5!*4! ways to arrange all the books like this.  <BR>\n" );
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document.write( "I think this is correct, but another tutor's opinion/verification might be a good idea.   </SPAN>\n" );
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