document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=548996>Question 548996</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am really lost with this concept:\r<BR>\n" );
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document.write( "Factorial expressions<BR>\n" );
document.write( "Find the value of the following:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%21+12%21%29%2F%288%2110%21%29 ALIGN=MIDDLE  ALT=\"%2811%21+12%21%29%2F%288%2110%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If your answer is not an integer, write it as an exact fraction. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357395 by </B><A HREF=/tutors/aboutme.mpl?userid=mathie123><B>mathie123(224)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathie123><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=357395\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We know that n!=n*(n-1)*(n-2)*...*2*1\r<BR>\n" );
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document.write( "So we can expand <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%21+12%21%29%2F%288%2110%21%29 ALIGN=MIDDLE  ALT=\"%2811%21+12%21%29%2F%288%2110%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%2A12%2A11%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29%2F%288%2A7%2A6%2A5%2A4%2A3%2A2%2A1%2A10%2A9%2A8%2A7%2A6%2A5%2A4%2A3%2A2%2A1%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now... looking at the expression above... can anything divide out (i.e. get rid of any number that appears in the numerator and denominator).  This leaves:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2811%2A12%2A11%2A10%2A9%29 ALIGN=MIDDLE  ALT=\"%2811%2A12%2A11%2A10%2A9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now this expression can be calculated as an integer on your calculator... I will leave that for you to do . \r<BR>\n" );
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document.write( "Obviously if we had large numbers... it wouldn't be a good idea to write out the whole factorial, but you may be able to see some patterns once you do some examples... (try to find them)\r<BR>\n" );
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document.write( "Hopefully this helps a bit... let me know if you are still unsure \r<BR>\n" );
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document.write( " </SPAN>\n" );
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