document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=465470>Question 465470</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the answer if the given is D={X,Y,Z} list the proper subsets </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #318976 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=318976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The proper subsets of a set are all subsets, including the null set, except the one subset that is identical to the given set.\r<BR>\n" );
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document.write( "You need the number of ways to select 0 things from 3 things, plus\r<BR>\n" );
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document.write( "The number of ways to select 1 thing from 3 things, plus\r<BR>\n" );
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document.write( "The number of ways to select 2 things from 3 things, but exclude\r<BR>\n" );
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document.write( "The number of ways to select 3 things from 3 things.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(3\cr 0\right\)\ +\ \left(3\cr 1\right\)\ +\ \left(3\cr 2\right\)\">\r<BR>\n" );
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document.write( "Where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \left(n\cr k\right\) \"> is the number of combinations of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> things taken <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> at a time and is calculated by <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{n!}{k!(n\,-\,k)!}\">\r<BR>\n" );
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document.write( "Hint:  Look at the 4th row of Pascal's triangle, and exclude the last element.\r<BR>\n" );
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document.write( "Now that you know the total number of proper subsets, you can determine if you have listed all of them and you can determine if you have made any duplications.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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