document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=237633>Question 237633</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 100C2 has a value of 4,950, what is the value of 100C98? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #174754 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=174754\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 100C2 has a value of 4,950, what is the value of 100C98?<BR>\n" );
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document.write( "It is the same number.<BR>\n" );
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document.write( "Why?<BR>\n" );
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document.write( "100C2 is a count of the number of sets of two you can draw<BR>\n" );
document.write( "from a set of 100 items.<BR>\n" );
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document.write( "But every time you draw a set of 2 from 100 you have<BR>\n" );
document.write( "automatically determined a set of 98 that you did <BR>\n" );
document.write( "not select.<BR>\n" );
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document.write( "The number of sets you did not select = the number<BR>\n" );
document.write( "of sets you collected.  So the count is the same.<BR>\n" );
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document.write( "In general nCk = nC(n-k)<BR>\n" );
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document.write( "Try it: 8C2 = (8*7)/(1*2) = 28<BR>\n" );
document.write( "8C6 = (8*7*6*5*4*3)/(1*2*3*4*5*6) = (8*7)/(1*2) = 28<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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