document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=787015>Question 787015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The US Senate consists of 13 women and 18 men.  If you randomly select five different senators.<BR>\n" );
document.write( "a. In how many possible ways can we select five senators out of this group?\r<BR>\n" );
document.write( "\n" );
document.write( "b. What is the probability that if we select five senators two of them are female?	 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #478049 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=478049\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> SOCIAL STUDIES NOTE:<BR>\n" );
document.write( "This maybe a good probability problem, but it would probably make most Social Studies teachers cry.<BR>\n" );
document.write( "The US Senate has 100 members, 2 for each of the 50 states.<BR>\n" );
document.write( "Maybe a committee of the Senate would be a small as 13+18=21 members.<BR>\n" );
document.write( "It would be hard to find 13 women in a Senate committee with 21 members, because we only have 20 women among the 100 Senators.<BR>\n" );
document.write( " <BR>\n" );
document.write( "MATH:<BR>\n" );
document.write( "Use combinations.<BR>\n" );
document.write( "a. There are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C31%2C5%29%29=31%2A30%2A19%2A28%2A27%2F%285%2A4%2A3%2A2%29=highlight%28169911%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ways to select 5 people from a group of 13+18=31 people<BR>\n" );
document.write( " <BR>\n" );
document.write( "b. There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C13%2C2%29%29=13%2A12%2F2=78 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2C13%2C2%29%29=13%2A12%2F2=78\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways to select 2 women from a group of 13 women.<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28matrix%282%2C1%2C18%2C3%29%29=18%2A17%2A16%2F%283%2A2%29=816 ALIGN=MIDDLE  ALT=\"%28matrix%282%2C1%2C18%2C3%29%29=18%2A17%2A16%2F%283%2A2%29=816\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways to select 3 men from a group of 18 men.<BR>\n" );
document.write( "So, there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=78%2A618=63648 ALIGN=MIDDLE  ALT=\"78%2A618=63648\"   DISABLED_style= \"max-width:90%; height:auto;\" > ways to select a subroup made of 2 women and 3 men from a group of 13 women and 18 men.<BR>\n" );
document.write( "Since there is a total of 169911 different subgroups of 5 people that could be formed from the same group of 13 women and 18 men, the probability of one of those  subgroups being one of the 78 with exactly 2 women is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=63648%2F169911=about0.3746 ALIGN=MIDDLE  ALT=\"63648%2F169911=about0.3746\"   DISABLED_style= \"max-width:90%; height:auto;\" > (or about 37.46%).<BR>\n" );
document.write( " <BR>\n" );
document.write( "DISCLAIMERS:<BR>\n" );
document.write( "I never was a Socials Studies teacher, and never even tried to be a teacher, but I did learn about US Government once.<BR>\n" );
document.write( "I would like to live to see the day that 13 out of every 31 US Senators are women, but we are still far from that ratio. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );