document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=770548>Question 770548</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A security code used to consist of two odd digits, followed by four even digits. To allow more codes to be generated, a new system uses two even digits, followed by any three digits. If repeated digits are allowed, the increase in the number of possible codes is____<BR>\n" );
document.write( "Answer: Old code: 5x5x5x5x5x5=15325<BR>\n" );
document.write( "        New code: 5x5x10x10x10=25000<BR>\n" );
document.write( "The increase in the number of codes is 9375.<BR>\n" );
document.write( "I don't understand why they use 5's and 10's!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #469562 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=469562\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "There are 10 possible digits, 0 through 9, for each place in the code.  But if a particular place must be either even or odd, then there are only 5 choices for that place -- because of the 10 possible digits, 5 of them are even and 5 of them are odd.\r<BR>\n" );
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document.write( "In the case of the old code, there are 5 ways to choose the first digit: it can either be 1, 3, 5, 7, or 9.  Then, for each of those choices, there are 5 ways to pick the second digit because you are allowed to repeat digits, namely 1, 3, 5, 7, and 9 again.  So just considering the first two positions, there are 5 times 5, which is to say 25 ways to fill them.  Then, the next position has 5 ways to fill it...0, 2, 4, 6, 8.  And so on.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "<font face=\"Math1\" size=\"+2\">Egw to Beta kai to Sigma</font><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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