document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=867481>Question 867481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given a group of students: G=(Allen,Brenda,Chad,Dorothy,Eric) or G=(A,B,C,D,E)count the different ways of choosing the following officers or representatives for student congress. Assume that no one can hold more than one office.\r<BR>\n" );
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document.write( "A president, a secretary, and a treasurer, if the president must be a woman and the other two must be men\r<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 #523076 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=523076\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are two women: Brenda and Dorothy (B, D)\r<BR>\n" );
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document.write( "There are three men: Allen, Chad, and Eric (A,C,E)\r<BR>\n" );
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document.write( "There are two ways to choose the president. This is because \"the president must be a woman\".\r<BR>\n" );
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document.write( "So we could start off with Brenda (B) to have B __  __ \r<BR>\n" );
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document.write( "The blank spaces represent slots for the secretary and treasurer.\r<BR>\n" );
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document.write( "There are 3 men to fill the second slot, then 3-1=2 men to fill the next slot. So 3*2 = 6 permutations possible. These permutations are:\r<BR>\n" );
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document.write( "BAC<BR>\n" );
document.write( "BCA<BR>\n" );
document.write( "BAE<BR>\n" );
document.write( "BEA<BR>\n" );
document.write( "BCE<BR>\n" );
document.write( "BEC\r<BR>\n" );
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document.write( "Note: order matters and BAC is different from BCA (since Allen is secretary and Chad is treasurer in BAC; but Chad is secretary and Allen is treasurer in BCA)\r<BR>\n" );
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document.write( "If we picked Dorothy for president, then we get\r<BR>\n" );
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document.write( "DAC<BR>\n" );
document.write( "DCA<BR>\n" );
document.write( "DAE<BR>\n" );
document.write( "DEA<BR>\n" );
document.write( "DCE<BR>\n" );
document.write( "DEC\r<BR>\n" );
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document.write( "There are 6 ways in the first group (with Brenda as president) and there are 6 ways in the second group (with Dorothy as president). \r<BR>\n" );
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document.write( "So there are 6+6 = <font color=\"red\">12</font> possible ways to have a president, a secretary, and a treasurer, if the president must be a woman and the other two must be men (given the candidates Allen,Brenda,Chad,Dorothy,Eric).<BR>\n" );
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