document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1110182>Question 1110182</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 10 students go hiking in pairs, how many different pairs of students are possible? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #725174 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=725174\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is the same as asking how many sets of 2 can you get out of a set of 10, where order within each set of 2 is not important.\r<BR>\n" );
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document.write( "that would the combination formula of c(10,2) = 10! / (2! * 8!)\r<BR>\n" );
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document.write( "that comes out to be c(10,2) = 45.\r<BR>\n" );
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document.write( "let each student be numbered from 0 to 9 and the possible pairings are shown below.\r<BR>\n" );
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document.write( "0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9<BR>\n" );
document.write( "1,2 1,3 1,4 1,5 1,6 1,7 1,8 1,9<BR>\n" );
document.write( "2,3 2,4 2,5 2,6 2,7 2,8 2,9<BR>\n" );
document.write( "3,4 3,5 3,6 3,7 3,8 3,9<BR>\n" );
document.write( "4,5 4,6 4,7 4,8 4,9<BR>\n" );
document.write( "5,6 5,7 5,8 5,9<BR>\n" );
document.write( "6,7 6,8 6,9<BR>\n" );
document.write( "7,8 7,9<BR>\n" );
document.write( "8,9\r<BR>\n" );
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document.write( "order not being important within each set of 2 means that the set of (1,0) and the set (0,1) are considered to be the same set and are therefore not counted as 2 separate sets.\r<BR>\n" );
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document.write( "that is why you only set the set (0,1) and do not see the set (1,0).\r<BR>\n" );
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document.write( "if order within each set of 2 was important, then you would have to see the set (0,1) and the set (1,0) as 2 separate sets.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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