document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1149230>Question 1149230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A die is loaded in such a way that the probability of the face with j dots<BR>\n" );
document.write( "turning up is proportional to j for j = 1,2,3,4,5,6. In 6 independent throws<BR>\n" );
document.write( "of this die, what is the probability that each face turns up exactly once? </SPAN>\n" );
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document.write( "1+2+3+4+5+6 = 21<br><BR>\n" );
document.write( "P(1) = 1/21<BR>\n" );
document.write( "P(2) = 2/21<BR>\n" );
document.write( "P(3) = 3/21<BR>\n" );
document.write( "P(4) = 4/21<BR>\n" );
document.write( "P(5) = 5/21<BR>\n" );
document.write( "P(6) = 6/21<br><BR>\n" );
document.write( "You need to get one of each outcome once.  The probability of doing that in any particular order is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F21%29%282%2F21%29%283%2F21%29%284%2F21%29%285%2F21%29%286%2F21%29 ALIGN=MIDDLE  ALT=\"%281%2F21%29%282%2F21%29%283%2F21%29%284%2F21%29%285%2F21%29%286%2F21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Those six outcomes can occur in any of 6! = 720 different orders.<br><BR>\n" );
document.write( "The probability of getting each outcome once in 6 rolls is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=720%2A%28%281%2F21%29%282%2F21%29%283%2F21%29%284%2F21%29%285%2F21%29%286%2F21%29%29+=+%28720%2A720%29%2F21%5E6 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That evaluates to 0.0060 to 4 decimal places, or very close to 0.6%.<br><BR>\n" );
document.write( " </SPAN>\n" );
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