document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=231056>Question 231056</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,\r<BR>\n" );
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document.write( "I always have trouble with word problems and I just want to make sure that I am doing this one correctly:\r<BR>\n" );
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document.write( "Eight horses are entered into a race. In how many ways can they cross the finish line, if ties are not allowed?\r<BR>\n" );
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document.write( "is it: 8*8*8*8*8*8*8*8 (8^8)\r<BR>\n" );
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document.write( "thank you for your help,<BR>\n" );
document.write( "Peter </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #171071 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=171071\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 8 horses can cross the finish line in 8! ways.\r<BR>\n" );
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document.write( "Consider 3 horses.\r<BR>\n" );
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document.write( "3! = 3*2*1 = 6 ways they can cross the finish line.\r<BR>\n" );
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document.write( "Those ways would be:\r<BR>\n" );
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document.write( "123<BR>\n" );
document.write( "132<BR>\n" );
document.write( "213<BR>\n" );
document.write( "231<BR>\n" );
document.write( "312<BR>\n" );
document.write( "321\r<BR>\n" );
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document.write( "Now consider 4 horses in a race.\r<BR>\n" );
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document.write( "The number of ways they can cross the finish line is 4!\r<BR>\n" );
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document.write( "4! = 4*3*2*1 = 24\r<BR>\n" );
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document.write( "Those ways are:\r<BR>\n" );
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document.write( "1234<BR>\n" );
document.write( "1243<BR>\n" );
document.write( "1324<BR>\n" );
document.write( "1342<BR>\n" );
document.write( "1423<BR>\n" );
document.write( "1432<BR>\n" );
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document.write( "2134<BR>\n" );
document.write( "2143<BR>\n" );
document.write( "2314<BR>\n" );
document.write( "2341<BR>\n" );
document.write( "2413<BR>\n" );
document.write( "2431<BR>\n" );
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document.write( "There should be 2 more sets of 6 which would make a total of 24.<BR>\n" );
document.write( "I'll do them just to show you.<BR>\n" );
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document.write( "3124<BR>\n" );
document.write( "3142<BR>\n" );
document.write( "3214<BR>\n" );
document.write( "3241<BR>\n" );
document.write( "3412<BR>\n" );
document.write( "3421<BR>\n" );
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document.write( "4123<BR>\n" );
document.write( "4132<BR>\n" );
document.write( "4213<BR>\n" );
document.write( "4231<BR>\n" );
document.write( "4312<BR>\n" );
document.write( "4321<BR>\n" );
document.write( "----\r<BR>\n" );
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document.write( "I think that does it.\r<BR>\n" );
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document.write( "For your problem, the numbers are too high to show each one separately, but the formula looks like it will do the trick so your answer is:\r<BR>\n" );
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document.write( "8! which equals 8*7*6*5*4*3*2*1\r<BR>\n" );
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document.write( "That equals 40,320 ways.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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