document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=563661>Question 563661</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if i have to pick two numbers from 1 to 10, provided the first number can't be greater than the second number. How many possible way I can represent the two number. Please suggest the formula to use? <BR>\n" );
document.write( "E.g. <BR>\n" );
document.write( "12 - valid<BR>\n" );
document.write( "21 - not valid </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #364979 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=364979\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If the 1st number is 1, the 2nd can be 2-10<BR>\n" );
document.write( "If the 1st number is 2, the 2nd can be 3-10<BR>\n" );
document.write( "If the 1st number is 3, the 2nd can be 4-10<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "This progression is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+9+%2B+8+%2B+7+%2B+6+%2B+5+%2B+4+%2B+3+%2B+2+%2B+1+=+45+ ALIGN=MIDDLE  ALT=\"+9+%2B+8+%2B+7+%2B+6+%2B+5+%2B+4+%2B+3+%2B+2+%2B+1+=+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "A formula would be if you can choose numbers <BR>\n" );
document.write( "from 1 to n, then the possible arrangements of 2 numbers<BR>\n" );
document.write( "the 1st being smaller than the 2nd<BR>\n" );
document.write( "is  (n-1) + (n-2) + (n-3) + . . . + 1<BR>\n" );
document.write( "This sum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29%2An%2A%28n-1%29+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29%2An%2A%28n-1%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "check:<BR>\n" );
document.write( "for 1 to 10, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%281%2F2%29%2A10%2A9+=+90%2F2+ ALIGN=MIDDLE  ALT=\"+%281%2F2%29%2A10%2A9+=+90%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+90%2F2+=+45+ ALIGN=MIDDLE  ALT=\"+90%2F2+=+45+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "OK\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );