document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203686>Question 1203686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain machine has nine switches mounted in a row. Each switch has three positions, a, b, and c.<BR>\n" );
document.write( "A) How many different settings are possible?<BR>\n" );
document.write( "B) Answer (a) if each position is used three times. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839453 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839453\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The presentation of part B is awkward at best; it appears to be asking the number of possible arrangements of the switch settings there are if there are three each in positions a, b, and c.<br><BR>\n" );
document.write( "The answer is then the number of distinct arrangements of the letters aaabbbccc; by a well-known counting principle, that number of arrangements is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%289%21%29%2F%28%283%21%29%283%21%29%283%21%29%29=362880%2F216=1680 ALIGN=MIDDLE  ALT=\"%289%21%29%2F%28%283%21%29%283%21%29%283%21%29%29=362880%2F216=1680\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: 1680<br><BR>\n" );
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