document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202956>Question 1202956</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A committee consisting of 3 men and 4 women is to be choose at random from 5 women and 6 men. What is the probability that one particular women and man will be on it. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838181 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838181\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "\"Choose\" the one particular man and one particular woman and put them on the committee.<br><BR>\n" );
document.write( "There are 4 women and 5 men left, from which you need to choose 2 men and 3 women: C(4,3)*C(5,2) = 4*10 = 40<br><BR>\n" );
document.write( "The total number of ways of choosing the last 5 members of the committee out of the remaining 9 people without restrictions is C(9,5) = 126<br><BR>\n" );
document.write( "ANSWER: 40/126 = 20/63<br><BR>\n" );
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document.write( "Revised answer after seeing the response from tutor @ikleyn....<br><BR>\n" );
document.write( "The above solution only makes sure that one particular man and one particular woman have to be on the committee; it overlooks the fact that the committee must contain 3 men and 4 women.<br><BR>\n" );
document.write( "Total number of ways of choosing 3 of the 6 men and 4 of the 5 women is<br><BR>\n" );
document.write( "C(6,3)*C(5,4) = 20*5 = 100<br><BR>\n" );
document.write( "So the answer to the question is 40/100 = 2/5 = 40% = 0.4<br><BR>\n" );
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