document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=952916>Question 952916</A>: <I><SPAN STYLE=\"word-break: break-all;\"> how many 5 digit counting  numbers contain at least one 6<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #581946 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=581946\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "We can divide all the five digit numbers into two groups.\r<BR>\n" );
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document.write( "One group which contains all such numbers which do not have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > at all, and the other group will be of such numbers which have at least one <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "These two groups or sets are complementary to each other. They together make the set of all <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5+ ALIGN=MIDDLE  ALT=\"5+\"   DISABLED_style= \"max-width:90%; height:auto;\" >digit numbers.\r<BR>\n" );
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document.write( "It is easy to calculate the number of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > digit numbers which do not contain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > at all. If we calculate this number and subtract it from the total number of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > digit numbers, we will get the required answer.\r<BR>\n" );
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document.write( "The total number of 5 digit numbers => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=99999+-+9999+=+90000 ALIGN=MIDDLE  ALT=\"99999+-+9999+=+90000\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Out of these, the number of 5 digit numbers which do <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > contain <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > at all is equal to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A9%2A9%2A9%2A9+=9%5E5=+59049 ALIGN=MIDDLE  ALT=\"9%2A9%2A9%2A9%2A9+=9%5E5=+59049\"   DISABLED_style= \"max-width:90%; height:auto;\" > (9 digits for each placeholder) \r<BR>\n" );
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document.write( "Therefore the number of five digit numbers which contain at least one <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90000+-59049+=+highlight%2830951%29 ALIGN=MIDDLE  ALT=\"90000+-59049+=+highlight%2830951%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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