document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=370342>Question 370342</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a.	Suppose we have a group of 8 students sitting on a long bench.<BR>\n" );
document.write( "Four of the eight insist on sitting side-by-side. In how many ways can the eight students be seated on the bench?\r<BR>\n" );
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document.write( "b.	Two of the eight insisting on not sitting side by side. In how many ways can the eight students be seated on the bench?\r<BR>\n" );
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document.write( "thanks alot </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #264009 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=264009\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. Suppose we have a group of 8 students sitting on a long bench.<BR>\n" );
document.write( "Four of the eight insist on sitting side-by-side. In how many ways can the eight students be seated on the bench?<BR>\n" );
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document.write( "Treat the four as a block that can be arranged 4! ways<BR>\n" );
document.write( "Treat the other four plus the block as 5 persons that<BR>\n" );
document.write( "can be arranged in 5! ways<BR>\n" );
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document.write( "Total arrangements = 4!*5! = 2880 arrangements<BR>\n" );
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document.write( "b. Two of the eight insisting on not sitting side by side. In how many ways can the eight students be seated on the bench?<BR>\n" );
document.write( "# of unrestricted arrangements = 8!<BR>\n" );
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document.write( "# of arrangements with the two sitting side-by-side = 14<BR>\n" );
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document.write( "Ans: 8!- 14 = 40,305<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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