document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166137>Question 1166137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 17 members on a board of directors. If they must form a subcommittee of 4 members, how many different subcommittees are possible?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790616 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=790616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are several different answers depending on how a subcommittee is formed.  For example, is it just four members of the board with equal status so that a committee consisting of Bill, Bob, Brian, and Basil is the same as one formed of Bob, Basil, Bill, and Brian?  Or does the subcommittee have a chairman so that a committee consisting of Chairman John plus Joe, Jill, and Jeri is different from one consisting of Chairman Jill plus Joe, John, and Jeri.  Perhaps there is a Chairman and a Chairman Pro Tem, so that Chairman Steve, Chairman Pro Tem Scott, Sally, and Sue...get the idea?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Assuming the first case, and using the formula for the number of combinations of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> things taken <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large r\"> at a time:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ {{n}\choose{r}}\ =\ \frac{n!}{(n\,-\,r)!r!}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "You need to calculate\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ {{17}\choose{4}}\">\r<BR>\n" );
document.write( "\n" );
document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src=\"http://c0rk.blogs.com/gr0undzer0/darwin-fish.jpg\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );