document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1127394>Question 1127394</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A catering service offers 12 appetizers, 5 main courses, and 6 desserts. A customer is to select 8 appetizers, 4 main courses, and 2 desserts for a banquet. In how many ways can this be done? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #743817 by </B><A HREF=/tutors/aboutme.mpl?userid=FrankM><B>FrankM(1040)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=FrankM><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=FrankM><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=743817\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a combination problem.\r<BR>\n" );
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document.write( "12C8 * 5C4 * 6C2 = 495*5*15 = 37125\r<BR>\n" );
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document.write( "Choosing 8 of the 12 apps starts as 12*11*10*9*8*7*6*5 which is 12!/4!, but this is a permutation, in which order matters, so the next step is to divide by 8! to get the correct result, 12C8 = 12!/(4!8!)  </SPAN>\n" );
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