document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1094038>Question 1094038</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If yu have 5 copies of one book 4 copies of each two books 6 copies each of three books and single copy of 8 book yu arrange it in_______no. Of ways  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #708677 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=708677\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>I will assume you mean arrange them on a shelf, in a single row....<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2B4%2B6%2B1%2B1%2B1%2B1%2B1%2B1%2B1%2B1%29%21%2F%28%285%21%29%284%21%29%286%21%29%281%21%29%281%21%29%281%21%29%281%21%29%281%21%29%281%21%29%281%21%29%281%21%29%29+=+23%21%2F%28%285%21%29%284%21%29%286%21%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "It's a general principle; let's look at a simple example: 3 copies of one book (\"A\"), 2 of another (\"B\"), and 1 of a third (\"C\").<br><BR>\n" );
document.write( "If all 6 books were different, the number of ways of arranging them would be 6!:<BR>\n" );
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document.write( "Imagine a list of all those 6! ways of arranging the 6 books.  The 3 A books can be ordered in 3! different ways.  That means every entry in the list occurs 3! times; so the list is too large by a factor of 3!.  So the number of arrangements is now<BR>\n" );
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document.write( "Likewise, the 2 B books can be arranged in 2! different ways, so again the list is too large by a factor of 2!; the number of distinct arrangements is now <BR>\n" );
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document.write( "And since there are no more books with multiple copies, that is the final number of distinct arrangements.<br><BR>\n" );
document.write( "In your problem, there are a total of 23 books, with 6 of one, 5 of another, and 4 of a third, with the rest being single books.  Thus the number shown at the beginning of my response.\r<BR>\n" );
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