document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1075613>Question 1075613</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag contains 16 fake diamonds and 8 real diamonds that are identically shaped. If 5 diamonds are randomly selected from the bag, what is the probability that 2 are fake and 3 are real? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #690259 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=690259\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The denominator is 24C5<BR>\n" );
document.write( "The numerator is 16C2*8C3; the numbers in front of the C add to 24 and behind add to 5.<BR>\n" );
document.write( "The probability is 120*56/42504=0.1581<BR>\n" );
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document.write( "Another way is to look at the probability the first is fake second fake, and other three not fake<BR>\n" );
document.write( "(16/24)*(15/23)*(8/22)(7/21)*(6/20).<BR>\n" );
document.write( "The denominator never changes, but the numerator can occur with 10 different orderings, FFRRR RRFFF etc. It is 5C2 or 5C3, both of which are 10.<BR>\n" );
document.write( "The above product is 0.01581, and multiplied by 10 gives 0.1581. </SPAN>\n" );
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