document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101050>Question 1101050</A>: <I><SPAN STYLE=\"word-break: break-all;\">  A teacher makes a multiple-choice quiz with 12 questions. 3 answers are A, 3 answers are B,2 answers are C and 4 answers are D. How many possible answer keys are possible\r<BR>\n" );
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document.write( "I think you can solve it like this but am not sure:\r<BR>\n" );
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document.write( "12C3 x 9C3 x 6C2 x 4C4<BR>\n" );
document.write( "= 277200 keys  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #715709 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=715709\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> for this problem, we use combinatorial counting\r<BR>\n" );
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document.write( "for the first question there are 12 possible choices, for the second question there are 11 choices, for the third question there are 10 possible choices, ...<BR>\n" );
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document.write( "Note that I assume there are NO restrictions on the placement of the answers<BR>\n" );
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document.write( "12! = 479001600<BR>\n" );
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document.write( "now we must divide 479001600 by the number of permutations we can not distinguish<BR>\n" );
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document.write( "479001600 / (3! * 3! * 2! * 4!) = 277200 possible answer keys<BR>\n" );
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