document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1119068>Question 1119068</A>: <I><SPAN STYLE=\"word-break: break-all;\"> .  An apartment building has 20 two-bedroom apartments and 8 three-bedroom apartments.  If 4 apartments are chosen at random to be redecorated, what are the probabilities that\r<BR>\n" );
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document.write( " a)	All will be two-bedroom apartments ?\r<BR>\n" );
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document.write( "(b)  2 will be two-bedroom apartments and 2 will be  three-bedroom apartments ?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #734512 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=734512\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The denominator is 28C4, choosing 4 apartments at random from 28.<BR>\n" );
document.write( "The numerator is 20C4, choosing only the two bedroom apartments.  The other part of the numerator would be the missing numbers 8C0, but 8C0=1, so it can be ignored.<BR>\n" );
document.write( "20C4/28C4=0.2366.<BR>\n" );
document.write( "The second will have numerator 20C2*8C2 with the same denominator.  Notice that the pre-Cs in the numerator add up to 28 and the post-Cs add up to 4.<BR>\n" );
document.write( "probability is 0.2598.<BR>\n" );
document.write( "Can check by looking at the other three possibilities, 0,1,3 are two bedroom.<BR>\n" );
document.write( "Those probabilities are 0.0547 with numerator 20C1*8C3<BR>\n" );
document.write( "and 0.0034 with numerator 20C0*8C4<BR>\n" );
document.write( "0.4454 with numerator 20C3*8C1.<BR>\n" );
document.write( "Those add to 1. </SPAN>\n" );
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