document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019519>Question 1019519</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 6 freshmen, 5 sophomores, 7 juniors, and 7 seniors are eligible to be on a committee.\r<BR>\n" );
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document.write( "In how many ways can a dance committee of 15 students be chosen if it is to consist of exactly 2 juniors and exactly 4 seniors, and the rest must be freshman or sophomores?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635460 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=635460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are C(7,2) = 21 ways of choosing 2 from 7 juniors.<BR>\n" );
document.write( "There are C(7,4) = 35 ways of choosing 4 from 7 seniors.<BR>\n" );
document.write( "After choosing 6 people, we have to choose 9 more students from the 6 freshmen and 5 sophomores.<BR>\n" );
document.write( "There are C(6,6)*C(5,3)+C(6,5)*C(5,4)+C(6,4)*C(5,5) = 10+30+15 = 55.<BR>\n" );
document.write( "Thus there are 21*35*55 = 40,425 ways to choose.<BR>\n" );
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