document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=580374>Question 580374</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Six students are to be chosen from a class of 18 to represent the class at a math contest. How many ways can the six students be chosen? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #371220 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=371220\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 18 ways to choose the first person\r<BR>\n" );
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document.write( "There are 17 ways to choose the second person (since a single person can't be chosen twice)\r<BR>\n" );
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document.write( "There are 16 ways to choose the third person\r<BR>\n" );
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document.write( "There are 15 ways to choose the fourth person\r<BR>\n" );
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document.write( "There are 14 ways to choose the fifth person\r<BR>\n" );
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document.write( "There are 13 ways to choose the sixth person\r<BR>\n" );
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document.write( "Multiply these all together to get: 18*17*16*15*14*13 = 13366080\r<BR>\n" );
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document.write( "So there are 13366080 different ways assuming order matters.\r<BR>\n" );
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document.write( "If order does NOT matter, then this means that you've been overcounting. To fix this issue, you need to divide by 6! = 6*5*4*3*2*1 = 720 to get\r<BR>\n" );
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document.write( "13366080/720 = 18564\r<BR>\n" );
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document.write( "So there are 18564 different ways assuming order does NOT matter. </SPAN>\n" );
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