document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190125>Question 1190125</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In how many ways can a family of 8 members be seated at a circular table with only 5 chairs? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821715 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Because the problem is stated incorrectly, the answer from the other tutor is correct: 0.<br><BR>\n" );
document.write( "8 people can't be seated in 5 chairs.<br><BR>\n" );
document.write( "Correct the statement of the problem:<br><BR>\n" );
document.write( "\"In how many ways can 5 members of a family of 8 be seated at a circular table with only 5 chairs?\"<br><BR>\n" );
document.write( "pick any one of the 5 seats to be the \"1st\" seat; there are 8 choices for the family member to sit in that seat<BR>\n" );
document.write( "pick any one of the remaining seats to be the \"2nd\" seat; there are 7 choices for the family member to sit in that seat<BR>\n" );
document.write( "pick any one of the remaining seats to be the \"3rd\" seat; there are 6 choices for the family member to sit in that seat<BR>\n" );
document.write( "pick either of the remaining seats to be the \"4th\" seat; there are 5 choices for the family member to sit in that seat<BR>\n" );
document.write( "there is only one remaining seat to be the \"5th\" seat; there are 4 choices for the family member to sit in that seat<br><BR>\n" );
document.write( "ANSWER (number of ways to seat 5 members of a family of 8 at a circular table with 5 chairs): 8*7*6*5*4 = 6720<br><BR>\n" );
document.write( "In the popular literature, it is likely that the \"expected\" correct answer is 6720/5 = 1344 -- the reason being that, when seated around a circular table, any one of the 5 chairs can be considered the \"first\".<br><BR>\n" );
document.write( "However, that is NOT how the problem is stated.<br><BR>\n" );
document.write( "The number of DIFFERENT ORDERS in which 5 members of a family of 8 can be seated around a circular table is 6720/5 = 1344.  But the number of DIFFERENT WAYS they can be seated is 6720.<br><BR>\n" );
document.write( "We can demonstrate the difference by considering the simple case of 3 people A, B, and C seated around a circular table:<br><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( "\r\n" );
document.write( "     A       A       B       B       C       C\r\n" );
document.write( "    B C     C B     A C     C A     A B     B A</PRE><BR>\n" );
document.write( "That is 6 different WAYS but only 6/3 = 2 different ORDERS.<br>\r<BR>\n" );
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