document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122883>Question 1122883</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From a faculty of six professors, six associate professors, ten assistant professors,<BR>\n" );
document.write( "and twelve instructors, a committee of size six is formed randomly. What is the<BR>\n" );
document.write( "probability that (a) there are exactly two professors on the committee; (b) all<BR>\n" );
document.write( "committee members are of the same rank? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739066 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=739066\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 34 total people, number of ways to choose six is 34C6=1344904 <BR>\n" );
document.write( "exactly two professors is 6C2, and ways to choose the rest are 28C4.  That product is 15*20475=307125, so probability overall is 0.2284\r<BR>\n" );
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document.write( "There is 1 way to choose 6 professors for the committee (all of them), 1 more way for all associate professors<BR>\n" );
document.write( "10C6 for the assistant professors (210) and 12C6 for the instructors, or 924.  Each of these is added for 1136 possibilities or probability 0.0008. </SPAN>\n" );
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