document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252101>Question 252101</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a die is loaded in such a way that the probabilityof the face with j dots turning up is proportional to j for j=1,2,3,4,5,6. in 6 independent throws of this die , what is the probability that each face turns up exactly one? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183876 by </B><A HREF=/tutors/aboutme.mpl?userid=vksarvepalli><B>vksarvepalli(154)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vksarvepalli><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=vksarvepalli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=183876\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the probability of face with 1 dot turning up be 1k<BR>\n" );
document.write( "the probability of face with 2 dots turning up  2k<BR>\n" );
document.write( "the probability of face with 3 dots turning up  3k\r<BR>\n" );
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document.write( "and so on\r<BR>\n" );
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document.write( "but since an outcome should be any one the face the sum of all these should be 1<BR>\n" );
document.write( "so,1k+2k+3k+4k+5k+6k=1\r<BR>\n" );
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document.write( "that is 21k=1\r<BR>\n" );
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document.write( "we get k= 1/21\r<BR>\n" );
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document.write( "now the probability that each face turns up exactly once in 6 throws is \r<BR>\n" );
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document.write( "1k*2k*3k*4k*5k*6k<BR>\n" );
document.write( "that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Factorial+6+%2A+k%5E6 ALIGN=MIDDLE  ALT=\"Factorial+6+%2A+k%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so the answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2F%2821%29%5E6 ALIGN=MIDDLE  ALT=\"720%2F%2821%29%5E6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or Factorial 6/21^6 </SPAN>\n" );
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