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 #27110 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27110\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We can see the pattern by looking at how many handshakes each person makes...<BR>\n" );
document.write( "The first person can shake 21 hands, the second person can shake 20 hands, since they already shook hands with person #1, the 3rd person does 19, the 4th 18, and so on...<BR>\n" );
document.write( "The sum of these 21 numbers is n(n+1) / 2 = 21(22) / 2 = 231.<BR>\n" );
document.write( "In terms of the 22 people, it becomes (n-1)n / 2, and that is the general expression you need in part c...<BR>\n" );
document.write( "Part b) Given there are 35 people, the number of shakes is 34(35) / = 17(35) = 595 handshakes... </SPAN>\n" );
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