document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209585>Question 1209585</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of ways to seat 3 students, 2 male teachers, and 4 female teachers around a round table with 10 chairs is how much?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849573 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52873)</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=849573\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "The number of ways to seat 3 students, 2 male teachers, and 4 female teachers <BR>\n" );
document.write( "around a round table with 10 chairs is how much?<BR>\n" );
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document.write( "For standard circular permutations, the general statement is:\r<BR>\n" );
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document.write( "    |                If there are n distinguishable objects,                          |\r\n" );
document.write( "    | then there are (n-1)! distinguishable circular permutations of these n objects. |\r\n" );
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document.write( "Since you came with more complicated problem with a vacant chair, you should be just <BR>\n" );
document.write( "familiar with these traditional problems with no vacant chairs.\r<BR>\n" );
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document.write( "In this problem, we have 3 students + 2 male teachers + 4 female teachers.<BR>\n" );
document.write( "They all are distinguishable objects. So, there are 3+2+4 = 9 distinguishable objects.\r<BR>\n" );
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document.write( "Plus to it, we have one chair, which is #10 distinguishable object.\r<BR>\n" );
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document.write( "Thus, the total of distinguishable objects in this problem is 10.<BR>\n" );
document.write( "All 10 objects are distinguishable and there are no repeating undistinguishable objects.\r<BR>\n" );
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document.write( "Therefore, according to the general statement, in this problem there are (10-1)! = 9!<BR>\n" );
document.write( "distinguishable circular permutations.\r<BR>\n" );
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document.write( "So, this given problem is similar/identical to just familiar to you other problems <BR>\n" );
document.write( "on circular permutations with distinguishable objects.\r<BR>\n" );
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document.write( "The difference appears when the number of undistinguishable objects in the problem<BR>\n" );
document.write( "(like undistinguishable vacant chairs) is 2 or more.  Then the value of different <BR>\n" );
document.write( "circular arrangement (n-1)!, where n is the number of all objects, in total, should be <BR>\n" );
document.write( "divided by  k!,  where k is the number undistinguishable objects (repeating copies). \r<BR>\n" );
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