document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1166385>Question 1166385</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A class has 4 seniors, 5 juniors, 3 sophomores, and 6 freshmen. If you randomly choose<BR>\n" );
document.write( "6 students, what is the probability that:\r<BR>\n" );
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document.write( "a. You choose at least 2 seniors?\r<BR>\n" );
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document.write( "b. You choose exactly 3 juniors and 3 freshman </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790893 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=790893\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> at least 2 seniors is 1-prob (1 senior) and prob (0 seniors)<BR>\n" );
document.write( "denominator is 18C6 and that is 18564\r<BR>\n" );
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document.write( "the numerator for the first  (1 senior) is (4C1)(14C5) since the other classes are not fixed.<BR>\n" );
document.write( "this is 4*2002 or 8008<BR>\n" );
document.write( "the numerators for 0 seniors is 14C6 and that is 3003<BR>\n" );
document.write( "so the probability of at least 2 seniors is 1-(11011)/18564=0.4069\r<BR>\n" );
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document.write( "Can check with 2, 3 or 4 seniors. for 3 it is 4C3 *14C3=1456 ways<BR>\n" );
document.write( "for 4 seniors it is 4C4*14C2=1*91=91<BR>\n" );
document.write( "for 2 seniors it is 4C2*14C4=6006<BR>\n" );
document.write( "that sum decided by 18564 gives a probability of 0.4069.\r<BR>\n" );
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document.write( "for b the numerator is 5C3*6C3 and that is 10*20=200<BR>\n" );
document.write( "the probability is 0.0108<BR>\n" );
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