document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1069630>Question 1069630</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ten new friends shake hands with each other once and once only.  How many total number of handshakes would there be?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #684829 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=684829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "<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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Each of 10 friends handshakes with each and all other 9 friends,\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and for each two pairs (a,b) and (b,a) we register only ONE handshake.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Therefore, we multiply 10 by 9 and then divide by 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The outcome is the same as the number of combinations of 10 items taken 2 at a time.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );