document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=282431>Question 282431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two of seven finalists will be selected and awarded $10,000 scholarships. In how many different ways can this final selection be made? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #205062 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=205062\">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( "Since the two prizes to be awarded are the same value, the order of selection does not matter.  Hence, you need the number of ways to select 2 things from 7 things.\r<BR>\n" );
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document.write( "The number of ways to select <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large k\"> things from <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\"> things where order doesn't matter is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \left(n\cr k\right)\ =\ \frac{n!}{k!(n\,-\,k)!}\">\r<BR>\n" );
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document.write( "Just substitute and do the arithmetic.\r<BR>\n" );
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document.write( "<b><i>Super Deluxe Double Plus Extra Credit</i></b>:  What is the difference in your answer if, instead of two $10,000 prizes, the committee was awarding a $13,000 prize and a $7,000 prize?\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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