document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191850>Question 1191850</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From a group of 6 men and 4 women we have to form a committee of 5 people how many committees are possible if there are to be 3 men and 2 women? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823712 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=823712\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The 3 men out of 6 can be chosen in any of \"6 choose 3\" ways: C(6,3).<br><BR>\n" );
document.write( "The 2 women out of 4 can be chosen in any of \"4 choose 2\" ways: C(4,2).<br><BR>\n" );
document.write( "We have to choose 3 of the 6 men AND 2 of the 4 women, so the numbers of ways of doing each get multiplied to find the answer.<br><BR>\n" );
document.write( "ANSWER: C(6,3)*C(4,2) = 20*6 = 120<br><BR>\n" );
document.write( "The total number of ways of choosing a committee of 5 of the 10 is C(10,5) = 252.  If you are new to doing the kinds of calculation required for this problem, it can be a good exercise to find all the different ways of selecting the committee (5 men and 0 women;  or 4 and 1; or 3 and 2 (the one we already did); or 2 and 3; or 1 and 4.  The sum of those different numbers of ways should be 252.<br><BR>\n" );
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