document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=2202>Question 2202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Congratulations! You have just won 25 video game tokens to use on these three challenging arcade gamse: Mighty Mediecal Monsters, Radical Racing Robots and Adventures Around the Amazon. All you have to do to collect your prize is answer this question: How many different ways are there to spend your 25 tokens on these three games provided that you play each game at least once? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #907 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=907\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Assume all the 25 tokens are the same, the three games use 25 tokens<BR>\n" );
document.write( " without caring the order as repeating combinations 3 different objects <BR>\n" );
document.write( " 25 times.<BR>\n" );
document.write( " Just like the number of positive integer solutions of the equation<BR>\n" );
document.write( "  X + Y + Z = 25<BR>\n" );
document.write( " Or equivalently<BR>\n" );
document.write( " X-1 + Y-1 + Z-1 = 22.<BR>\n" );
document.write( " Since X-1 >=0, Y-1>=0,and Z-1>=0(means each game at least once)\r<BR>\n" );
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document.write( " There are H(3,22) = C(3+22-1,22) = C(24,22) = 24*23/2 = 276...Answer\r<BR>\n" );
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