document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=391386>Question 391386</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How many different 5 digit codes are possible using the keypad show ,if the frist digit cannot be 0 and no digit may be use more than one? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #277681 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</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=277681\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=five ALIGN=MIDDLE  ALT=\"five\"   DISABLED_style= \"max-width:90%; height:auto;\" > digit codes using <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > digits, first one can't be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "think of choices per digit - they <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=can%27t ALIGN=MIDDLE  ALT=\"can%27t\"   DISABLED_style= \"max-width:90%; height:auto;\" > repeat, so one digit is used each time\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+%2A+9+%2A+8+%2A+7+%2A+6=27216 ALIGN=MIDDLE  ALT=\"9+%2A+9+%2A+8+%2A+7+%2A+6=27216\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Well, basically all you do in this problem is multiply.<BR>\n" );
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document.write( "- put down <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > blank spaces on paper and then put the number of combinations in each space. \r<BR>\n" );
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document.write( "For example, there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" > total digits that can be used (0-9). \r<BR>\n" );
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document.write( "However the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=first ALIGN=MIDDLE  ALT=\"first\"   DISABLED_style= \"max-width:90%; height:auto;\" > digit can not be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > possible combinations (1-9). \r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=second ALIGN=MIDDLE  ALT=\"second\"   DISABLED_style= \"max-width:90%; height:auto;\" > digit cannot be the same as the first digit, but it can be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > combinations. \r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=third ALIGN=MIDDLE  ALT=\"third\"   DISABLED_style= \"max-width:90%; height:auto;\" > digit cannot be either the first or the second digit and thus there are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > combinations. \r<BR>\n" );
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document.write( "The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=fourth ALIGN=MIDDLE  ALT=\"fourth\"   DISABLED_style= \"max-width:90%; height:auto;\" > digit has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   DISABLED_style= \"max-width:90%; height:auto;\" > combinations and the fifth has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+ ALIGN=MIDDLE  ALT=\"6+\"   DISABLED_style= \"max-width:90%; height:auto;\" >combinations. so if you multiply the\r<BR>\n" );
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document.write( " numbers of combinations you should have \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9+x+9+x+8+x+7+x+6+=+27216 ALIGN=MIDDLE  ALT=\"9+x+9+x+8+x+7+x+6+=+27216\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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