document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=473736>Question 473736</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A city council with nine members must appoint a three person subcommittee. How many subcommittees 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 #324948 by </B><A HREF=/tutors/aboutme.mpl?userid=ccs2011><B>ccs2011(207)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ccs2011><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=ccs2011><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=324948\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This will be solved using combinations because there is no order within the sub-committees. <BR>\n" );
document.write( "How many groups of 3 can be made from 9 members.<BR>\n" );
document.write( "Combination formula:<BR>\n" );
document.write( "9C3 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%21%2F%28%289-3%29%21%2A3%21%29+=+9%21%2F%286%21%2A3%21%29 ALIGN=MIDDLE  ALT=\"9%21%2F%28%289-3%29%21%2A3%21%29+=+9%21%2F%286%21%2A3%21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "9! can be written as 9*8*7*6!<BR>\n" );
document.write( "Notice that the 6! can be cancelled on top and bottom, leaving<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%2A8%2A7%29%2F%283%2A2%2A1%29 ALIGN=MIDDLE  ALT=\"%289%2A8%2A7%29%2F%283%2A2%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can simplify things by doing more cancelling, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F3+=+3 ALIGN=MIDDLE  ALT=\"9%2F3+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8%2F2+=+4 ALIGN=MIDDLE  ALT=\"8%2F2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A4%2A7+=+12%2A7+=+84 ALIGN=MIDDLE  ALT=\"3%2A4%2A7+=+12%2A7+=+84\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore there are 84 sub-committees possible. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );