document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=492772>Question 492772</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The dean of an Engineering School invites all 9 chairpersons and their spouses to his house for a Winter Solstice party.  If each department chair may attend without a spouse, but the spouse may not attend without the department chair, how many different sets of attendees are possible? \r<BR>\n" );
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document.write( "[b] Think of another way to count the possible sets of attendees.  If you can, also write the two approaches as a combinatorial identity.\r<BR>\n" );
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document.write( "Again I'm lost as to how to begin setting this problem up.<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 #335208 by </B><A HREF=/tutors/aboutme.mpl?userid=sudhanshu_kmr><B>sudhanshu_kmr(1152)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=sudhanshu_kmr><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=sudhanshu_kmr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=335208\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "Each chairperson can attend the party in 3 ways:<BR>\n" );
document.write( "a) only chairperson\r<BR>\n" );
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document.write( "b) Chairperson and spouse\r<BR>\n" );
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document.write( "c) none of both.\r<BR>\n" );
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document.write( "total no. of ways = 3*3*...*3 = 3^9 = 19683\r<BR>\n" );
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