document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1118015>Question 1118015</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the probability if you randomly select 6 people from 7 men and 7 women that will have at least 3 women in the group? \r<BR>\n" );
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document.write( "The answer my teach gave us is 302/429 or 0.704\r<BR>\n" );
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document.write( "I've tried many ways but I can't figure out how to get this answer. Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #733195 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=733195\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You should post what you've tried, so a tutor can see where you are getting stuck.<br>\r<BR>\n" );
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document.write( "By considering the complementary problem (2 or fewer women), the problem is computationally easier:<BR>\n" );
document.write( "P(3 or more women are chosen) = 1 - P(2 or less women are chosen) <br>\r<BR>\n" );
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document.write( "P(exactly 0 women are chosen) = (C(7,0)*C(7,6)) / C(14,6)<BR>\n" );
document.write( "P(exactly 1 woman is chosen) =  (C(7,1)*C(7,5)) / C(14,6)<BR>\n" );
document.write( "P(exactly 2 women are chosen) = (C(7,2)*C(7,4)) / C(14,6)\r<BR>\n" );
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document.write( "Where C(n,r) = n! / ((n-r)!*r!) <br>\r<BR>\n" );
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document.write( "Compute the above three values, add them all together, then subtract the result from 1 to arrive at 0.704.  <BR>\n" );
document.write( "[ If you work with the fractions, note that the denominator will be 3003 (= 7*429) ] \r<BR>\n" );
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document.write( "覧覧覧覧覧予r<BR>\n" );
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document.write( "Tutor ikleyn has missed this: for each selection of three or more women, there are N>0 selections of men that increase the numerator in a multiplicative fashion.  For example, W1,W2,W3,M1,M2,M3  is different than W1,W2,W3,M1,M2,M4  even though the same three women are selected in both cases.  <br>\r<BR>\n" );
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document.write( "The numerator in fact should be  C(7,3)*C(7,3) + C(7,4)*C(7,2) + C(7,5)*C(7,1) + C(7,6)*C(7,0)  = 2114.    These represent the number of ways of selecting 3 women and 3 men, plus 4 women and 2 men,  etc.<BR>\n" );
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document.write( "There you have your teacher's fraction, as  2114/3003 = (7*302) / (7*429)  \r<BR>\n" );
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