document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=773503>Question 773503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the number of ways in which a man can invite one or more of his 8 friends to dinner </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #471605 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=471605\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> He can have 1 friend for dinner<BR>\n" );
document.write( "He can have 2 friends for dinner<BR>\n" );
document.write( "He can have 3 friends for dinner <BR>\n" );
document.write( "and so on up to<BR>\n" );
document.write( "He can have 8 friends for dinner<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "In each of these 8 cases, use the<BR>\n" );
document.write( "formula for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%288%2Cr%29+ ALIGN=MIDDLE  ALT=\"+C%288%2Cr%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r+ ALIGN=MIDDLE  ALT=\"+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <BR>\n" );
document.write( "the number of friends invited <BR>\n" );
document.write( "to dinner. Note that you don't use<BR>\n" );
document.write( "permutations since the order of<BR>\n" );
document.write( "the invited friends doesn't matter<BR>\n" );
document.write( "----------------------------<BR>\n" );
document.write( "So, the solution is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%288%2C1%29+%2B+C%288%2C2%29+%2B+C%288%2C3%29+%2B+C%288%2C4%29+ ALIGN=MIDDLE  ALT=\"+C%288%2C1%29+%2B+C%288%2C2%29+%2B+C%288%2C3%29+%2B+C%288%2C4%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "etc. up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%288%2C8%29+ ALIGN=MIDDLE  ALT=\"+C%288%2C8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%288%2C1%29+=+8%21+%2F+%28+1%21%2A%28+8-1+%29%21+%29+ ALIGN=MIDDLE  ALT=\"+C%288%2C1%29+=+8%21+%2F+%28+1%21%2A%28+8-1+%29%21+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%288%2C1%29+=+8%21%2F7%21+ ALIGN=MIDDLE  ALT=\"+C%288%2C1%29+=+8%21%2F7%21+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%288%2C1%29+=+8+ ALIGN=MIDDLE  ALT=\"+C%288%2C1%29+=+8+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%288%2C2%29+=+8%21+%2F+%28+2%21%2A%28+8+-+2+%29%21+%29+ ALIGN=MIDDLE  ALT=\"+C%288%2C2%29+=+8%21+%2F+%28+2%21%2A%28+8+-+2+%29%21+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%288%2C2%29+=+8%21+%2F+%28+2%2A1%2A6%2A5%2A4%2A3%2A2%2A1+%29 ALIGN=MIDDLE  ALT=\"+C%288%2C2%29+=+8%21+%2F+%28+2%2A1%2A6%2A5%2A4%2A3%2A2%2A1+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%288%2C2%29+=+%28+8%2A7+%29+%2F+2+ ALIGN=MIDDLE  ALT=\"+C%288%2C2%29+=+%28+8%2A7+%29+%2F+2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%288%2C2%29+=+28+ ALIGN=MIDDLE  ALT=\"+C%288%2C2%29+=+28+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Continue up to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+C%288%2C8%29+ ALIGN=MIDDLE  ALT=\"+C%288%2C8%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > and add up<BR>\n" );
document.write( "all the results. <BR>\n" );
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document.write( " </SPAN>\n" );
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