document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190792>Question 190792</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 8 Physics books, 4 calculus books, 7 us history textbooks, and 3 resource books on a shelf.  Assuming the books in each category are NOT DISTINCT how many ways can they be arranged on the shelf? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143278 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=143278\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 8 Physics books, 4 calculus books, 7 us history textbooks, and 3 resource books on a shelf.  Assuming the books in each category are NOT DISTINCT how many ways can they be arranged on the shelf?<BR>\n" );
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document.write( "There are 22 positions to be filled.<BR>\n" );
document.write( "# of ways to pick 8 places for the physics: 22C8<BR>\n" );
document.write( "# of ways to pick 4 places for the calc: 14C4<BR>\n" );
document.write( "# of ways to pick 7 places for the hist: 10C7<BR>\n" );
document.write( "# of ways to pick 3 for the resource: 3C3<BR>\n" );
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document.write( "Total number of arrangements : Multiply the four factors<BR>\n" );
document.write( "I get 3.84108 X 10^10<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );