document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=844392>Question 844392</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 12 videotapes arranged in a row on a shelf in a video shop. There are three identical copies of Gone with the wind, 4 of Tootsie and 5 of Gladiator. *<BR>\n" );
document.write( "(i)How many different arrangements of videotapes are there? (Is it 12! ?)<BR>\n" );
document.write( "(ii) How many different arrangements are there if videos with the same titles are grouped together?<BR>\n" );
document.write( "(iii) The 12 videotapes are arranged at random in a ow of the shelf. Find the probability that the arrangement has a copy of Gone with the Wind, at the end of one row, and a copy of Gladiator at the other end. <BR>\n" );
document.write( "Thanks!! :)  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #508739 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=508739\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 12 videotapes arranged in a row on a shelf in a video shop. <BR>\n" );
document.write( "There are three identical copies of Gone with the wind, 4 of Tootsie and 5 of Gladiator. <BR>\n" );
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document.write( "(i)How many different a! = 6rrangements of videotapes are there?<BR>\n" );
document.write( "Ans: 12!/(3!*4!*5!) = 27720 ways<BR>\n" );
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document.write( "(ii) How many different arrangements are there if videos with the same titles are grouped together?<BR>\n" );
document.write( "Ans: 3! = 6<BR>\n" );
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document.write( "(iii) The 12 videotapes are arranged at random in a row of the shelf. Find the probability that the arrangement has a copy of Gone with the Wind, at the end of one row, and a copy of Gladiator at the other end. <BR>\n" );
document.write( "# of ways to succeed: 3*5*(10!/(2!*4!*4!)) = 47250<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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