document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096554>Question 1096554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If you were to solve at least 1 but at most 5 problems from this set of 10 problems, how many problem subsets are there that may be solved? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #710988 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=710988\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>You need to choose either 1, 2, 3, 4, or 5 of the 10 problems.  The numbers of ways to do that are \"10 choose 1\", \"10 choose 2\", ..., and \"10 choose 5\".<br><BR>\n" );
document.write( "The easiest way to find those numbers is to look at the 5th row of Pascal's Triangle, which begins<BR>\n" );
document.write( "1, 10, 45, 120, 210, 252, ...<br><BR>\n" );
document.write( "Those numbers are 10 choose 0, 10 choose 1, ..., 10 choose 4, and 10 choose 5.<br><BR>\n" );
document.write( "So the number of ways to choose at least 1 and at most 5 problems is<BR>\n" );
document.write( "10+45+120+210+252 = 637 </SPAN>\n" );
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