document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=418849>Question 418849</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help me please?? Thank You!!<BR>\n" );
document.write( "20) H ow many different sequences of 4 digits are possible if the first digit<BR>\n" );
document.write( "must be 3, 4, or 5 and if the sequence may not end in 000? Repetition of<BR>\n" );
document.write( "digits is allowed.\r<BR>\n" );
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document.write( "A) 2 ,997 <BR>\n" );
document.write( "B) 2 ,999<BR>\n" );
document.write( "C) 2 ,000 <BR>\n" );
document.write( "D) 1 ,512 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #293031 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=293031\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I would compute all the possibilities as if there<BR>\n" );
document.write( "were no restrictions. Then I would subtract the<BR>\n" );
document.write( "choices that are not allowed<BR>\n" );
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document.write( "With no restrictions:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%2A10%2A10%2A10+=+10%5E4+ ALIGN=MIDDLE  ALT=\"+10%2A10%2A10%2A10+=+10%5E4+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---------<BR>\n" );
document.write( "0,1,2,6,7,8, and 9 are not allowed <BR>\n" );
document.write( "for the 1st digit. That is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7%2A10+%2A10+%2A10++=+7%2A10%5E3 ALIGN=MIDDLE  ALT=\"+7%2A10+%2A10+%2A10++=+7%2A10%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > not allowed<BR>\n" );
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document.write( "With the last 3 digits 0,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10%2A1+=+10 ALIGN=MIDDLE  ALT=\"+10%2A1+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > not allowed<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E4+-+7%2A10%5E3+-+10+=+3000+-+10+ ALIGN=MIDDLE  ALT=\"10%5E4+-+7%2A10%5E3+-+10+=+3000+-+10+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+3000+-+10+=+2990+ ALIGN=MIDDLE  ALT=\"+3000+-+10+=+2990+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now the tricky part: When I tested for sequences not allowed<BR>\n" );
document.write( "did I count some things twice ? If I did, I have to add those back in.<BR>\n" );
document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7%2A10+%2A10+%2A10++=+7%2A10%5E3 ALIGN=MIDDLE  ALT=\"+7%2A10+%2A10+%2A10++=+7%2A10%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > not allowed includes<BR>\n" );
document.write( "0000, 1000, 2000, 6000, 7000, 8000, and 9000<BR>\n" );
document.write( "so, I must add these back in<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2990+%2B+7+=+2997+ ALIGN=MIDDLE  ALT=\"+2990+%2B+7+=+2997+\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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