document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1042549>Question 1042549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> One evening, n men enter the restaurant and put their hats at the reception. Each man gets a random hat back <BR>\n" );
document.write( "when going back after having dinner. Find the expected number of men who get their right hat back.\r<BR>\n" );
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document.write( "A. 1\r<BR>\n" );
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document.write( "B. 1/2\r<BR>\n" );
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document.write( "C. 1/n\r<BR>\n" );
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document.write( "D. n/2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #657619 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52805)</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=657619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "One evening, n men enter the restaurant and put their hats at the reception. Each man gets a random hat back <BR>\n" );
document.write( "when going back after having dinner. Find the expected number of men who get their right hat back.<BR>\n" );
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document.write( "It is a good problem and the formulation is good.\r<BR>\n" );
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document.write( "But, in order to be solved, it should be reformulated in mathematically correct form.\r<BR>\n" );
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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( "In my view, this correct formulation is as follows.\r\n" );
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document.write( "Among n! permutations of \"n\" numbers 1, 2, 3, . . . , n how many are those where the number \"k\" is in the k-th place (in k-th position) ?\r\n" );
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document.write( "Then the answer is obvious: there are (n-1)! of such permutations.\r\n" );
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document.write( "And we are interested in this ratio <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28n-1%29%21%2Fn%21 ALIGN=MIDDLE  ALT=\"%28n-1%29%21%2Fn%21\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fn ALIGN=MIDDLE  ALT=\"1%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "<U>Answer</U>.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fn ALIGN=MIDDLE  ALT=\"1%2Fn\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Option C.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "On permutations, read the lesson\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Permutations/Introduction-to-Permutations.lesson>Introduction to Permutations</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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