document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=239061>Question 239061</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are  entrees 17 available at a restaurant. From these, Archie is to choose  4 for his party. How many groups of 4 entrees can he choose, assuming that the order of the entrees chosen does not matter?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #175580 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=175580\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 17! / (4!*13!) = 17*16*15*14*13!/(4!*13!) = 17*16*15*14/(4*3*2) = 17*2*5*14 = 2380\r<BR>\n" );
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document.write( "smaller number lets you see it better.\r<BR>\n" );
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document.write( "assume 2 out of 5\r<BR>\n" );
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document.write( "5!/2!3! = 5*4/2 = 10\r<BR>\n" );
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document.write( "let abcde be the possible choice of entrees.\r<BR>\n" );
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document.write( "possible sets of 4 combinations (order not important) are:\r<BR>\n" );
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document.write( "ab<BR>\n" );
document.write( "ac<BR>\n" );
document.write( "ad<BR>\n" );
document.write( "ae<BR>\n" );
document.write( "bc<BR>\n" );
document.write( "bd<BR>\n" );
document.write( "be<BR>\n" );
document.write( "cd<BR>\n" );
document.write( "ce<BR>\n" );
document.write( "de\r<BR>\n" );
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document.write( "your problem is the same with bigger numbers.\r<BR>\n" );
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document.write( "the formula for number of combinations is:\r<BR>\n" );
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document.write( "n! / (x!*(n-x)!)\r<BR>\n" );
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document.write( "where\r<BR>\n" );
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document.write( "n is the total number of possible entrees<BR>\n" );
document.write( "x is the number of entrees in each set.\r<BR>\n" );
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document.write( "your formula becomes:\r<BR>\n" );
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document.write( "17! / ((4!*(17-4)!) which becomes:\r<BR>\n" );
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document.write( "17! / (4!*13!) as shown above.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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