document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=867360>Question 867360</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A task force studying sex discrimination wishes to establish a subcommittee. If the subcommittee is to consist of 11 members chosen at random from a group of 15 men and 18 women, find the probability that the subcommittee consists of the following?<BR>\n" );
document.write( "(a) 8 men and 3 women (Round your answer to two decimal places.)\r<BR>\n" );
document.write( "\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "(b) all women (Round your answer to seven decimal places.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522972 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=522972\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 15+18 = 33 people total. So there are 33 C 11 = 193,536,720 ways to form a committee of 11 people (with no restrictions on gender). \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I'm using the <a  rel=nofollow HREF=\"http://www.mathwords.com/c/combination_formula.htm\">combination formula</a> to compute 33 C 11. It's faster to do with a calculator, but I recommend you do a few by hand to get an idea of how it works.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------<BR>\n" );
document.write( "a)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are 15 C 8 = 6,435 ways to pick 8 men (from a pool of 15 men)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are 18 C 3 = 816 ways to pick 3 women (from a pool of 18 women)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are 6,435*816 = 5,250,960 ways to pick a committee of 11 people where there are 8 men and 3 women.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Divide this by the total number of ways to form an 11 member committee: 5,250,960/193,536,720 = 0.02713159549258\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then round to two decimal places: 0.02713159549258 ----> <font color=\"red\">0.03</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the probability of selecting exactly 8 men and 3 women is <font color=\"red\">0.03</font> \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------------------------------<BR>\n" );
document.write( "b) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are 18 C 11 = 31,824 ways to pick a committee of all women.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Divide this by the total number of ways to form an 11 member committee: 31,824/193,536,720 = 0.00016443391208\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Then round to seven decimal places: 0.00016443391208 ----> <font color=\"red\">0.0001644</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the probability of selecting all women, ie a committee of 11 women, is <font color=\"red\">0.0001644</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );