document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=858584>Question 858584</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How can 5000! (a large factorial) be found numerically? <BR>\n" );
document.write( "Someone, call him Igor for this problem :) Anyway - wants to know how<BR>\n" );
document.write( "many groups of 50 are there in 5000. <BR>\n" );
document.write( "I started working this using nCr =  n! / r!(n-r)!<BR>\n" );
document.write( "nCr = 5000C50, and chose to settle for a ball-park (estimated figure) quote,<BR>\n" );
document.write( "yet have no idea although the number C must lie between astronomical and &#8734;.<BR>\n" );
document.write( "50! is solvable, but was wondering if 5000! can be partitioned or reduced<BR>\n" );
document.write( "so a hand calculator could work it. Any shortcuts here would be appreciated! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #517285 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=517285\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You do not need to calculate a number as astronomical as 5000!,<BR>\n" );
document.write( "because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%21%2F%285000-50%29%21=5000%21%2F4950%21=5000%2A4999%2A4998%2A%22...%22%2A4953%2A4952%2A4951 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and that is slightly less astronomical.<BR>\n" );
document.write( "According to the combinations function in the Excel spreadsheet program in my computer, 5000C50 is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.2839%2A10%5E120 ALIGN=MIDDLE  ALT=\"2.2839%2A10%5E120\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That must also an estimate, because there is no way it could calculate all 120 decimal places.<BR>\n" );
document.write( "I also calculated 5000C50 as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%2A4999%2A4998%2A%22...%22%2A4953%2A4952%2A4951%2F50%21=6.9432%2A10%5E184%2F%283.04141%2A10%5E64%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Excel also calculated <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%2A4999%2A4998%2A%22...%22%2A4953%2A4952%2A4951=6.9432%2A10%5E184 ALIGN=MIDDLE  ALT=\"5000%2A4999%2A4998%2A%22...%22%2A4953%2A4952%2A4951=6.9432%2A10%5E184\"   DISABLED_style= \"max-width:90%; height:auto;\" > for me.<BR>\n" );
document.write( "I do not know if you can do that with a calculator.<BR>\n" );
document.write( "A crude approximation of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%21%2F4950%21=5000%2A4999%2A4998%2A%22...%22%2A4953%2A4952%2A4951 ALIGN=MIDDLE  ALT=\"5000%21%2F4950%21=5000%2A4999%2A4998%2A%22...%22%2A4953%2A4952%2A4951\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%5E50=%285%2A1000%29%5E50=%285%2A10%5E3%29%5E50=5%5E50%2A10%5E150=8.8178%2A10%5E34%2A10%5E150=8.8178%2A10%5E184 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "A better approximation for<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%2A%284999%2A4951%29%2A%284998%2A1952%29%2A%22...%22%2A%284976%2A4974%29%2A4975=5000%2A%284975%5E2-24%5E2%29%2A%284975%5E2-23%5E2%29%2A%22...%22%2A%284975%5E2-1%5E2%29%2A4975 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5000%2A4975%5E49=6.9475%2A10%5E184 ALIGN=MIDDLE  ALT=\"5000%2A4975%5E49=6.9475%2A10%5E184\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );