document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208263>Question 1208263</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In how many ways can 3 female teachers, 2 female students, and 2 male students be arranged around a round table such that there is a female student between each pair of female teachers?\" </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846570 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "In how many ways can 3 female teachers, 2 female students, and 2 male students <BR>\n" );
document.write( "be arranged around a round table such that there is a female student <BR>\n" );
document.write( "between each pair of female teachers?<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Wording is monstrous, but I will try to do my best.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "I will use a symbol F            as a placeholder for female teachers;\r\n" );
document.write( "           a symbol G (as girls) as a placeholder for female students;\r\n" );
document.write( "           a symbol B (as boys)  as a placeholder for male students.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "As problem is worded, the only way to satisfy requirements is to have a block\r\n" );
document.write( "FGFGF at circular siting.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Also, I will use a symbol D for this block FGFGF, when I will consider this block as one clued object.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then \r\n" );
document.write( "\r\n" );
document.write( "    - there are 3! = 6 ways/permutations for 3 distinguished female teachers (F) inside this block; \r\n" );
document.write( "\r\n" );
document.write( "    - there are 2! = 2 ways/permutations for 2 distinguished female students (G) inside this block;\r\n" );
document.write( "\r\n" );
document.write( "   -  in circular sitting, we can assume that the block D = FGFGF is in position \"North\", or 12 o'clock.\r\n" );
document.write( "      \r\n" );
document.write( "      Then in circular sitting, there is only one possible remaining configuration  DGG, or  FGFGFBB.\r\n" );
document.write( "\r\n" );
document.write( "       Finally, since 2 permutations are possible for two distinguishable boys, it gives an additional factor 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Now the number of all possible arrangements is 3! * 2! * 2! = 6*2*2 = 24.    <U>ANSWER</U>\r\n" );
document.write( "</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "Solved.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "In this my solution, I considered participating people as distinguishable individuals.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "///////////////////////\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Why did I say that wording is monstrous ?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Because on a circle, there is NO such notion and such conception as \"between two points\".\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "It is and it makes sense for points on a line, but not on a circle.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So, a reader more rigorous mathematically than me could advise you <BR>\n" );
document.write( "to through this problem away or, at least, to edit (to write) it properly.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This writing is good for those readers what are able to read the thoughts of a writer<BR>\n" );
document.write( "immediately from the writer's head or \"between the lines\", or \"behind the lines\", which is not Math.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );