document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=481474>Question 481474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> pls help me solve this problem in probability... thank you..\r<BR>\n" );
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document.write( "a ring of keys can hold 7 keys. In how many ways can the keys be arranged if the ring can be turned over? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #329704 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=329704\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> ring of keys can hold 7 keys.<BR>\n" );
document.write( "the keys are a,b,c,d,e,f,g<BR>\n" );
document.write( "the possible number of arrangements would be 7! = 7*6*5*4*3*2*1 = 5040.<BR>\n" );
document.write( "let's see what happens if there are only 3 keys.<BR>\n" );
document.write( "the number of arrangements would be 3! = 3*2 = 6<BR>\n" );
document.write( "those arrangements would be:<BR>\n" );
document.write( "a,b,c<BR>\n" );
document.write( "a,c,b<BR>\n" );
document.write( "b,a,c<BR>\n" );
document.write( "b,c,a<BR>\n" );
document.write( "c,a,b<BR>\n" );
document.write( "c,b,a<BR>\n" );
document.write( "if you turn the ring over, then:<BR>\n" );
document.write( "a,b,c becomes c,b,a<BR>\n" );
document.write( "a,c,b becomes b,c,a<BR>\n" );
document.write( "b,a,c becomes c,a,b<BR>\n" );
document.write( "b,c,a becomes a,c,b<BR>\n" );
document.write( "c,a,b becomes b,a,c<BR>\n" );
document.write( "c,b,a becomes a,b,c<BR>\n" );
document.write( "since all these arrangements are already accounted for, there are no new arrangements that are created by flipping the ring over.<BR>\n" );
document.write( "i would say that you get the same number of ways the keys can be arranged whether or not the ring can be turned over.<BR>\n" );
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