document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=191344>Question 191344</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 10 houses in your neighborhood having a yard sale. You want to go to at least 5 of the houses having a yard sale. How many different combinations of yard sales can you attend?\r<BR>\n" );
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document.write( "My answer choices are:\r<BR>\n" );
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document.write( "A) 386<BR>\n" );
document.write( "B) 638<BR>\n" );
document.write( "C) 848<BR>\n" );
document.write( "D) 1,286<BR>\n" );
document.write( "E) 9,858,240 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #143606 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=143606\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "For this you need combinations.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  C^n_k = {n \choose k} = \frac{n!}{k!(n - k)!} = 252\">\r<BR>\n" );
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document.write( "If you wanted to visit exactly 5 of the 10, the answer would be\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \  C^{10}_{5} = {10 \choose 5} = \frac{10!}{5!(10 - 5)!} = 252\">\r<BR>\n" );
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document.write( "But you want to visit <i><b>at least</b></i> 5, which means you may do 6, 7, 8, 9 or even all 10.\r<BR>\n" );
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document.write( "So, to <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE {10 \choose 5}\"> you must add <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE {10 \choose 6}\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE {10 \choose 7}\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE {10 \choose 8}\">, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE {10 \choose 9}\">, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE {10 \choose 10}\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ {10 \choose 5} + {10 \choose 6} + {10 \choose 7} + {10 \choose 8} + {10 \choose 9} + {10 \choose 10}\">\r<BR>\n" );
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document.write( "Man, that's a lot of arithmetic.  I'm glad I don't have to do it.  But here is a shortcut if you have MS Excel on your computer.  Pick a cell on an empty spreadsheet and type in:  =combin(10,5)  then hit the enter key.  You will get 252.  Then copy the same thing to 5 adjacent cells and go back in and edit the second number to be 6, then 7 and so on.  Then sum all 6 cells.\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" );
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