document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042202>Question 1042202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help on parts A through C please. Its confusing.\r<BR>\n" );
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document.write( "5.  8 people, consisting of four women and four men (four man-woman couples) are going to stand in a line for a dance picture.  How many different ways can they…\r<BR>\n" );
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document.write( "a)  line-up for a picture?  ______________________________\r<BR>\n" );
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document.write( "b)  line-up if they alternate man/woman/man/….OR woman/man/woman…..?______________________<BR>\n" );
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document.write( "c)  line up if all couples stand side-by-side?  _____________________________<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 #657164 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20056)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><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=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=657164\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\"><b>\r\n" );
document.write( "(a) any of the 8 people can stand in any of the 8 positions from\r\n" );
document.write( "the left-most position all the way to the right-most position.\r\n" );
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document.write( "1. Choose the person to stand left-most in 8 ways.\r\n" );
document.write( "2. Choose the person to stand 2nd from the left as any of the \r\n" );
document.write( "   7 people who haven't yet been chosen. That can be done in 7 \r\n" );
document.write( "   ways.  So the first 2 positions can be filled in 8*7 ways.\r\n" );
document.write( "3. Choose the person to stand 3rd from the left as any of the \r\n" );
document.write( "   6 people who haven't yet been chosen. That can be done in 6 \r\n" );
document.write( "   ways.  So the first 3 positions can be filled in 8*7*6 ways.\r\n" );
document.write( "4. Choose the person to stand 4th from the left as any of the \r\n" );
document.write( "   5 people who haven't yet been chosen. That can be done in 5 \r\n" );
document.write( "   ways.  So the first 4 positions can be filled in 8*7*6*5 ways.\r\n" );
document.write( "5. Choose the person to stand 4th from the right as any of the \r\n" );
document.write( "   4 people who haven't yet been chosen. That can be done in 4 \r\n" );
document.write( "   ways.  So the first 5 positions can be filled in 8*7*6*5*4 ways.\r\n" );
document.write( "6. Choose the person to stand 3rd from the right as any of the \r\n" );
document.write( "   3 people who haven't yet been chosen. That can be done in 3 \r\n" );
document.write( "   ways.  So the first 6 positions can be filled in 8*7*6*5*4*3 ways.\r\n" );
document.write( "7. Choose the person to stand 2nd from the right as either of the \r\n" );
document.write( "   2 people who haven't yet been chosen. That can be done in 2 \r\n" );
document.write( "   ways.  So the first 7 positions can be filled in 8*7*6*5*4*3*2 ways.\r\n" );
document.write( "8. Choose the person to stand right-most as the 1 person who hasn't \r\n" );
document.write( "   yet been chosen. That can be done in only 1 way.  So all 8 \r\n" );
document.write( "   positions can be filled in 8*7*6*5*4*3*2*1 ways.\r\n" );
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document.write( "That's 8*7*6*5*4*3*2*1 = 8! = 40320 ways.\r\n" );
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document.write( "I won't go into so much detail on the others.\r\n" );
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document.write( "b) line-up if they alternate man/woman/man/….OR woman/man/woman…..?<BR>\n" );
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document.write( "1.  Choose whether MWMWMWMW or WMWMWMWM in 2 ways.\r\n" );
document.write( "2.  Choose the men to stand in 4! ways.\r\n" );
document.write( "3.  Choose the women to stand in 4! ways.\r\n" );
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document.write( "That 2*4!*4! = 2*24*24 = 1152 ways. \r\n" );
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document.write( "c) line up if all couples stand side-by-side? _____________________________<BR>\n" );
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document.write( "1. Choose the left-most couple 4 ways.\r\n" );
document.write( "2. Choose whether the man is left of the woman or\r\n" );
document.write( "   right of the woman in 2 ways.\r\n" );
document.write( "3. Choose the next to left-most couple 3 ways.\r\n" );
document.write( "4. Choose whether the man is left of the woman or\r\n" );
document.write( "   right of the woman in 2 ways.\r\n" );
document.write( "5. Choose the next to right-most couple 2 ways.\r\n" );
document.write( "6. Choose whether the man is left of the woman or\r\n" );
document.write( "   right of the woman in 2 ways.\r\n" );
document.write( "7. Choose the right-most couple 1 way.\r\n" );
document.write( "8. Choose whether the man is left of the woman or\r\n" );
document.write( "   right of the woman in 2 ways.\r\n" );
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document.write( "4*2*3*2*2*2*1*2 = 384 ways.\r\n" );
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document.write( "Edwin</PRE></b> </SPAN>\n" );
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