document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75963>Question 75963</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose a City Council consist of 4 men and 5 women.\r<BR>\n" );
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document.write( "a.  In how many ways can the City Council members be lined up for a group picture?<BR>\n" );
document.write( "I'm not sure if I did this right, but here is how I approached this problem. <BR>\n" );
document.write( "9x8x7x6x5x4x3x2x1=362,880\r<BR>\n" );
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document.write( "I was confused on these.<BR>\n" );
document.write( "b.  In how many ways can they be lined up if the men and women must alternate?<BR>\n" );
document.write( "c.  In how many ways can they be lined up with the men together and the women together?<BR>\n" );
document.write( "d.  In how many ways can they be arranged if two rows are used with the women in the front row and the men in the back row? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54554 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=54554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your answer to (a) looks correct.<BR>\n" );
document.write( "As to (b), the only way the men and women can alternate is if<BR>\n" );
document.write( "women are at both ends. If you try putting a man at one end, you<BR>\n" );
document.write( "end up putting 2 women together. So it goes<BR>\n" );
document.write( "W M W M W M W M W<BR>\n" );
document.write( "There are 5 possible ways to put a woman in the 1st position<BR>\n" );
document.write( "There are 4 possible ways to put a man in the 2nd position<BR>\n" );
document.write( "There are 4 possible ways to put a woman in the 3rd position<BR>\n" );
document.write( "There are 3 possible ways to put a man in the 4th position<BR>\n" );
document.write( "There are 3 possible ways to put a woman in the 5th position<BR>\n" );
document.write( "There are 2 possible ways to put a man in the 6th position<BR>\n" );
document.write( "There are 2 possible ways to put a woman in the 7th position<BR>\n" );
document.write( "There is 1 possible way to put a man in the 8th position<BR>\n" );
document.write( "There is 1 possible way to put a woman in the 9th position<BR>\n" );
document.write( "The product of all the possibilities is the answer<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A4%2A4%2A3%2A3%2A2%2A2%2A1%2A1+=+2880 ALIGN=MIDDLE  ALT=\"5%2A4%2A4%2A3%2A3%2A2%2A2%2A1%2A1+=+2880\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer<BR>\n" );
document.write( "(c) If the women and men are grouped together, It looks like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A3%2A2%2A1+=+24 ALIGN=MIDDLE  ALT=\"4%2A3%2A2%2A1+=+24\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible ways to arrange the men and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A4%2A3%2A2%2A1+=+120 ALIGN=MIDDLE  ALT=\"5%2A4%2A3%2A2%2A1+=+120\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible ways to arrange the women<BR>\n" );
document.write( "All the possible combos is the product <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2A120+=+2880 ALIGN=MIDDLE  ALT=\"24%2A120+=+2880\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "But this isn't the final answer. For every combo, the group<BR>\n" );
document.write( "of men can be on the left or the right, so I think the<BR>\n" );
document.write( "correct answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A24%2A120+=+5760 ALIGN=MIDDLE  ALT=\"2%2A24%2A120+=+5760\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And (d) is the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24%2A120+=+2880 ALIGN=MIDDLE  ALT=\"24%2A120+=+2880\"   DISABLED_style= \"max-width:90%; height:auto;\" > because you can't interchange the <BR>\n" );
document.write( "groups of men and women.  </SPAN>\n" );
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