document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1191462>Question 1191462</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Topics In Contemporary Math<BR>\n" );
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document.write( "Permutations and Combinations\r<BR>\n" );
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document.write( "QUESTION 10\r<BR>\n" );
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document.write( "The 2015 Tour de France had 198 cyclists enter.  How many top three finishes were possible? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823296 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=823296\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "There are 198 choices for first place, 197 for second, and 196 for third. We count down until we fill all three slots.<BR>\n" );
document.write( "Then we multiply those values.\r<BR>\n" );
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document.write( "198*197*196 = <font color=red>7,645,176</font>\r<BR>\n" );
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document.write( "You could use the nPr permutation formula, but make sure to simplify and cancel out the factorial terms. If you were to use a calculator with a built in nPr function, then it might signal an error because factorials get really big even for relatively small values of n. It's perhaps best to stick to the first method mentioned.\r<BR>\n" );
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document.write( "Answer: <font color=red>7,645,176</font><BR>\n" );
document.write( "This number is a little over 7.6 million.<BR>\n" );
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