document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1098386>Question 1098386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the design of a certain mechanical product, ten components are to be stacked into a cylindrical casing, in a manner that minimizes the impact of shocks. One end of the casing is designated as the top and the other end is the bottom.\r<BR>\n" );
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document.write( "a. If all components are different, how many different stacks are possible?<BR>\n" );
document.write( "b. If six components are identical to one another, but the others are different, how many different stacks are possible?<BR>\n" );
document.write( "c. If four components are of one type and identical to one another, and four components are of another type and identical to one another, but the others are different, how many different designs are possible? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #712776 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=712776\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "In the design of a certain mechanical product, ten components are to be stacked into a cylindrical casing, in a manner <BR>\n" );
document.write( "that minimizes the impact of shocks. One end of the casing is designated as the top and the other end is the bottom.\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "a.  If all components are different, how many different stacks are possible?\r\n" );
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document.write( "    10! = 10*9*8*7*6*5*4*3*2*1 = 3628800  different stacks.\r\n" );
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document.write( "b.  If six components are identical to one another, but the others are different, how many different stacks are possible?\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%21%2F6%21 ALIGN=MIDDLE  ALT=\"10%21%2F6%21\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 10*9*8*7 = 5040  different stacks.\r\n" );
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document.write( "c.  If four components are of one type and identical to one another, and four components are of another type \r\n" );
document.write( "    and identical to one another, but the others are different, how many different designs are possible?\r\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%21%2F%284%21%2A4%21%29 ALIGN=MIDDLE  ALT=\"10%21%2F%284%21%2A4%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6300  different stacks.\r\n" );
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