document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1099798>Question 1099798</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The parents of 5 students are invited to attend their graduation ceremony. They are arranged to be seated in a row of 10 VIP seats. How many ways can they be seated if any 3 pairs of parents are to be seated to their own spouse.\r<BR>\n" );
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document.write( "ANS from tutorial bk : 403200 ( i just need to show steps )  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #714393 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=714393\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "(1) Choose the 3 pairs of parents out of the total of 5 pairs to be the ones that will be seated next to their spouses: C(5,3) = 10 {\"5 choose 3\").<BR>\n" );
document.write( "(2)Treat each of the three pairs as units; then the number of ways of arranging those 3 units and the other 4 single parents is 7! = 5040.<BR>\n" );
document.write( "(3) In each of the 3 pairs, the two spouses can be arranged in either of 2 ways: 2*2*2 = 8.<br><BR>\n" );
document.write( "All together, the total number of ways of arranging the 10 people is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2A5040%2A8+=+403200 ALIGN=MIDDLE  ALT=\"10%2A5040%2A8+=+403200\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "IMPORTANT NOTE:<br><BR>\n" );
document.write( "I used your given answer to get that result.<br><BR>\n" );
document.write( "As the problem is written, I think the answer should be different -- because in many of the 7! arrangements of the 3 pairs of parents and the other 4 parents (step (2) above), other pairs of spouses will be seated next to each other.  But the problem IMPLIES that EXACTLY 3 pairs of parents are supposed to be seated next to each other.<br><BR>\n" );
document.write( "Counting the number of ways in that case would be far more complicated.... </SPAN>\n" );
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