document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1008174>Question 1008174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If a customer purchases a new stereo system during the spring sale, he may choose any 4 CDs from 24 classical and 40 jazz selections. In how many ways can the customer choose 2 of each? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #623989 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=623989\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 24c2 * 40c2 = 215280\r<BR>\n" );
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document.write( "ncx is the combination formula of extracting x out of n where order is not important.\r<BR>\n" );
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document.write( "ncx = n! / (x! * (n-x)!)\r<BR>\n" );
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document.write( "24c2 = 24! / (2! * 22!) = (24*23*22!) / (2!*22!) = (24*23)/2! = 12*23 = 276\r<BR>\n" );
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document.write( "40c2 = 40! / (2! * 38!) = (40*39*38!) / (2! * 38!) = (40*39)/2! = 20*39 = 780\r<BR>\n" );
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document.write( "276 * 780 = 215280.\r<BR>\n" );
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document.write( "if you want to see how this works, use much smaller numbers.\r<BR>\n" );
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document.write( "assume 3 of each.\r<BR>\n" );
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document.write( "you get 3c2 * 3c2 = 3*3 = 9\r<BR>\n" );
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document.write( "let abc be the 3 possible selections of classical.<BR>\n" );
document.write( "let 123 be the 3 possible selections of jazz.\r<BR>\n" );
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document.write( "3c2 of abc = ab, ac, bc<BR>\n" );
document.write( "3c2 of 123 = 12, 13, 23\r<BR>\n" );
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document.write( "3c2 * 3c2 = 9 becomes:\r<BR>\n" );
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document.write( "ab12<BR>\n" );
document.write( "ab13<BR>\n" );
document.write( "ab23\r<BR>\n" );
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document.write( "ac12<BR>\n" );
document.write( "ac13<BR>\n" );
document.write( "ac23\r<BR>\n" );
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document.write( "bc12<BR>\n" );
document.write( "bc13<BR>\n" );
document.write( "bc23\r<BR>\n" );
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document.write( "the same concept works with the much larger numbers.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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