document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=41948>Question 41948</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If every person in our class shakes hands with every other perison in the class exactly once\r<BR>\n" );
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document.write( "(a)  How many handshakes will have taken place if there are 22 studemts in the class<BR>\n" );
document.write( "(b)  If there were 35 students in the class, how many handshakes would there be?<BR>\n" );
document.write( "(c)  What if there were n people? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27107 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27107\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose there were 'n' people.<BR>\n" );
document.write( "Then each shook hands with (n-1) people.<BR>\n" );
document.write( "So total number of handshakes = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%28n-1%29%2F2 ALIGN=MIDDLE  ALT=\"n%28n-1%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "[Why divided by 2? The answer is whether person A shakes hand with person B or person B shakes hand with person A is immaterial as these two situations refer to a single handshake.]\r<BR>\n" );
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document.write( "For 22 and 35 students put n = 22 and 35 respectively and you will get 231 and 595 handshakes accordingly. </SPAN>\n" );
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