document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=272662>Question 272662</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A computer password consist of six characters.The first two must be lower case letters and the remaining four can be either digits or lower case letters. how many different passwords are possible?<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 #199375 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=199375\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 26 letters in  the alphabet.<BR>\n" );
document.write( "first 2 must be lower case letters so 26*26 are all possibilities.<BR>\n" );
document.write( "remaining 4 can be lower case letters or digits.<BR>\n" );
document.write( "10 digits from 0 to 9 makes 26 + 10 = 36 possibilities for each position.<BR>\n" );
document.write( "total should be:\r<BR>\n" );
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document.write( "26^2 * 36^4 = 1.135420416 * 10^9 possibilities.\r<BR>\n" );
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document.write( "that's equivalent to 1,135,420,416 possibilities (1 trillion, 135 billion, 420 million, 416).\r<BR>\n" );
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document.write( "to see how this works, use much smaller numbers.\r<BR>\n" );
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document.write( "assume 5 positions total<BR>\n" );
document.write( "assume first 3 positions can each be one of 2 letters only (a or b).<BR>\n" );
document.write( "assume next 2 positions can each be one of 2 letters only plus 1 number (a or b or 1).\r<BR>\n" );
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document.write( "possibilities are 2^3 * 3^2 = 8 * 9 = 72\r<BR>\n" );
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document.write( "possibilities for the first 3 positions would be:\r<BR>\n" );
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document.write( "aaa<BR>\n" );
document.write( "bbb<BR>\n" );
document.write( "aab<BR>\n" );
document.write( "baa<BR>\n" );
document.write( "aba<BR>\n" );
document.write( "abb<BR>\n" );
document.write( "bba<BR>\n" );
document.write( "bab\r<BR>\n" );
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document.write( "total of 8\r<BR>\n" );
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document.write( "possibilities for the next 2 positions would be:\r<BR>\n" );
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document.write( "aa<BR>\n" );
document.write( "bb<BR>\n" );
document.write( "ab<BR>\n" );
document.write( "ba<BR>\n" );
document.write( "a1<BR>\n" );
document.write( "1a<BR>\n" );
document.write( "b1<BR>\n" );
document.write( "1b<BR>\n" );
document.write( "11\r<BR>\n" );
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document.write( "total of 9\r<BR>\n" );
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document.write( "when you combine the first 3 positions with the last 2 positions, you can get a total of 8 * 9 different possibilities.\r<BR>\n" );
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document.write( "example of 2 of the possibilities when you combine the first 3 positions and the last 2 positions would be:\r<BR>\n" );
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document.write( "aaaaa<BR>\n" );
document.write( "aaabb<BR>\n" );
document.write( "aaaab<BR>\n" );
document.write( "aaaba<BR>\n" );
document.write( "aaaa1<BR>\n" );
document.write( "aaa1a<BR>\n" );
document.write( "aaab1<BR>\n" );
document.write( "aaa1b<BR>\n" );
document.write( "aaa11\r<BR>\n" );
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document.write( "+\r<BR>\n" );
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document.write( "bbbaa<BR>\n" );
document.write( "bbbbb<BR>\n" );
document.write( "bbbab<BR>\n" );
document.write( "bbbba<BR>\n" );
document.write( "bbba1<BR>\n" );
document.write( "bbb1a<BR>\n" );
document.write( "bbbb1<BR>\n" );
document.write( "bbb1b<BR>\n" );
document.write( "bbb11\r<BR>\n" );
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document.write( "+\r<BR>\n" );
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document.write( "6 more of these gives you the 8 * 9 total possibilities.\r<BR>\n" );
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document.write( "same principle applies to the larger set of numbers in your problem.\r<BR>\n" );
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