document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=275509>Question 275509</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 6 people running the 100 meter dash. How many different orders can the runners finish? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #200928 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=200928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 6! = 6*5*4*3*2*1 = 720 possible ways.\r<BR>\n" );
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document.write( "assume it was only 3 people.\r<BR>\n" );
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document.write( "that would be 3! = 3*2*1 = 6\r<BR>\n" );
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document.write( "let the people be abc.\r<BR>\n" );
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document.write( "order of finish possible would be:\r<BR>\n" );
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document.write( "abc<BR>\n" );
document.write( "acb<BR>\n" );
document.write( "bac<BR>\n" );
document.write( "bca<BR>\n" );
document.write( "cab<BR>\n" );
document.write( "cba\r<BR>\n" );
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document.write( "this is called a permutation because order is important.\r<BR>\n" );
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document.write( "assume it was 4 people.\r<BR>\n" );
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document.write( "number of ways would be 4! = 4*3*2*1 = 24\r<BR>\n" );
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document.write( "possible ways get a lot bigger after 4.\r<BR>\n" );
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document.write( "assume the people were abcd\r<BR>\n" );
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document.write( "possible ways would be:\r<BR>\n" );
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document.write( "abcd<BR>\n" );
document.write( "abdc<BR>\n" );
document.write( "acbd<BR>\n" );
document.write( "acdb<BR>\n" );
document.write( "adbc<BR>\n" );
document.write( "adcb<BR>\n" );
document.write( "bacd<BR>\n" );
document.write( "badc<BR>\n" );
document.write( "bcad<BR>\n" );
document.write( "bcda<BR>\n" );
document.write( "bdac<BR>\n" );
document.write( "bdca<BR>\n" );
document.write( "cabd<BR>\n" );
document.write( "cadb<BR>\n" );
document.write( "cbad<BR>\n" );
document.write( "cbda<BR>\n" );
document.write( "cdab<BR>\n" );
document.write( "cdba<BR>\n" );
document.write( "dabc<BR>\n" );
document.write( "dacb<BR>\n" );
document.write( "dbac<BR>\n" );
document.write( "dbca<BR>\n" );
document.write( "dcab<BR>\n" );
document.write( "dcba\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );