document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=999315>Question 999315</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i have invited nine people to a party. They all shake hands with me, and each pair shake hands. how many hand shakes are there?<BR>\n" );
document.write( "9+8+7+6+5+4+3+2+1=45<BR>\n" );
document.write( "how many hand shakes would there be if i invited n-1 people?\r<BR>\n" );
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document.write( "I organise another party with 9 guests and myself. some pairs shook hands, but some did not. no pair shook hands more than once. Must there be two people who shook hands with the same number of people? what if i had invited n-1 people?\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #616994 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52782)</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=616994\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "i have invited nine people to a party. They all shake hands with me, and each pair shake hands. how many hand shakes are there?<BR>\n" );
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document.write( "The answer is &nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n%2A%28n-1%29%29%2F2 ALIGN=MIDDLE  ALT=\"%28n%2A%28n-1%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. &nbsp;&nbsp;&nbsp;&nbsp;(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%5Bn%5D%5E2 ALIGN=MIDDLE  ALT=\"C%5Bn%5D%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, &nbsp;if you know what does it mean).\r<BR>\n" );
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document.write( "If &nbsp;n = 9+1 = 10, &nbsp;then the number of hand shakes is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2A9%29%2F2 ALIGN=MIDDLE  ALT=\"%2810%2A9%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 45.\r<BR>\n" );
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document.write( "This is very standard problem on combinations.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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