document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=883539>Question 883539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many necklaces can be made from 6 beads of different colors?<BR>\n" );
document.write( "the answer is 60, but how? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #533602 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=533602\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 6 beads in that necklace and each one is a different color.<BR>\n" );
document.write( "Identify the colors by the codes 1, 2, 3, 4, 5, and 6.<BR>\n" );
document.write( "Lay the necklace on the table and look for the bead of color 6.<BR>\n" );
document.write( "What are the other colors read clockwise from that bead?<BR>\n" );
document.write( "Is it 12345? 15324? Some other sequence<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%21=5%2A4%2A3%2A2=120 ALIGN=MIDDLE  ALT=\"5%21=5%2A4%2A3%2A2=120\"   DISABLED_style= \"max-width:90%; height:auto;\" > such sequences.<BR>\n" );
document.write( " <BR>\n" );
document.write( "However, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12345 ALIGN=MIDDLE  ALT=\"12345\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54321 ALIGN=MIDDLE  ALT=\"54321\"   DISABLED_style= \"max-width:90%; height:auto;\" > represent the same necklace flipped over.<BR>\n" );
document.write( "By laying the necklace on the table we made it easier to count the possibilities, but we counted each one twice.<BR>\n" );
document.write( "There are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120%2F2=highlight%2860%29 ALIGN=MIDDLE  ALT=\"120%2F2=highlight%2860%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible necklaces.<BR>\n" );
document.write( " <BR>\n" );
document.write( "NOTE:<BR>\n" );
document.write( "Your teacher wants you to mention \"permutations\".<BR>\n" );
document.write( "It is just one of many names/words (hopefully not too many) that they will make you learn. Words and symbols help us communicate more efficiently, as long as we use them just as necessary. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );