document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1069980>Question 1069980</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem: A gambler places a bet on a horse race. To win, she must pick the top three finishers in any order. Thirteen horses of equal ability are entered in the race. Assuming the horses finish in a random order, what is the probability that the gambler will win her bet?\r<BR>\n" );
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document.write( "My Attempt: First, I calculated in how many ways ( Combination) can we pick 3 horses out of 13. My answer was 286.\r<BR>\n" );
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document.write( "I then calculated in how many ways we can order the top 3 finishers ( with permutations). I got 6 ways. \r<BR>\n" );
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document.write( "My answer was 6/286=3/143.\r<BR>\n" );
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document.write( "My answer was wrong, though. The correct answer was 1/286.... Where might have I went wrong? Thanks in Advance! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #685076 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=685076\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> So the total number of finishes is calculated by, <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=13%2A12%2A11=1716 ALIGN=MIDDLE  ALT=\"N=13%2A12%2A11=1716\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The gambler wins if she picks the top three horses in any order.\r<BR>\n" );
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document.write( "There are 6 ways for the three winners to be arranged in the top three.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=6%2F1716=1%2F286 ALIGN=MIDDLE  ALT=\"P=6%2F1716=1%2F286\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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