document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891173>Question 891173</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 12. There are 20 quarts of milk on a supermarket shelf, four of which are spoiled. A customer buys three quarts of milk.<BR>\n" );
document.write( "(a) How many samples are possible?<BR>\n" );
document.write( "(b) How many samples contain exactly two quarts of spoiled milk? <BR>\n" );
document.write( "(c) How many samples contain at least two quarts of spoiled milk?<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 #539567 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=539567\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 20 quarts of milk on a supermarket shelf.<BR>\n" );
document.write( "4 of them are spoiled.<BR>\n" );
document.write( "That means 16 good and 4 bad.\r<BR>\n" );
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document.write( "A customer buys 3 quarts of milk.\r<BR>\n" );
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document.write( "Total possible samples that are different from each other is given by the formula of C(20,4) = 20! = 4845\r<BR>\n" );
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document.write( "Total possible samples that contain exactly 2 quarts of bad milk are equal to C(4,2) * C(16,1) = 6 * 16 = 96\r<BR>\n" );
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document.write( "Total possible samples that contain exactly 3 quarts of bad milk are equal to C(4,3) = 4\r<BR>\n" );
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document.write( "Total possible samples that contain at least 2 quarts of bad milk are equal to C(4,2) * C(16,1) + C(4,3) = 96 + 4 = 100\r<BR>\n" );
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document.write( "C(n,x) = n! / ((n-x)! * x!)\r<BR>\n" );
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document.write( "For Example:\r<BR>\n" );
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document.write( "C(4,2) = 4! / (2! * 2!) = 4*3*2*1 / 2*1*2*1 = 6\r<BR>\n" );
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document.write( "C(16,1) = 16 * 15! / (1! * 15!) = 16 / 1 = 16.\r<BR>\n" );
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document.write( "C(4,3) = 4! / (1!*3!) = 4*3*2*1 / 1*3*2*1 = 4\r<BR>\n" );
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