document.write( "Question 1200970: A password must be 6, 7, or 8 characters long, and may include capital letters, lower- case letters, or digits. In how many ways could this be done
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\n" ); document.write( "b)with no repetition permitted?
\n" ); document.write( "c)if at least one of the characters in part a) must be a digit?
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Algebra.Com's Answer #835197 by ikleyn(52780) $\"\"$ $\"About$

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\n" ); document.write( "A password must be 6, 7, or 8 characters long, and may include capital letters,
\n" ); document.write( "lower-case letters, or digits. In how many ways could this be done
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\n" ); document.write( "(b) with no repetition permitted?
\n" ); document.write( "(c) if at least one of the characters in part a) must be a digit?
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document.write( "(a) In this case, the total number of symbols is 26+26+10 = 62.\r\n" );
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document.write( "    Each of these 62 symbols can be in any position, independently.\r\n" );
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document.write( "    So, the number of passwords  of the length 6 is       (1)\r\n" );
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document.write( "                                 of the length 7 is       (2)\r\n" );
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document.write( "                                 of the length 8 is       (3)\r\n" );
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document.write( "                                 of the length 6, or 7 or 8  is the sum of number (1), (2) and (3)\r\n" );
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document.write( "          N(a) =  +  + .  ANSWER\r\n" );
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document.write( "(b) In this case, the total number of symbols is still the same 26+26+10 = 62.\r\n" );
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document.write( "    The number of passwords  of the length 6 is  62*61*60*59*58*57         (4)\r\n" );
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document.write( "                             of the length 7 is  62*61*60*59*58*57*56      (5)\r\n" );
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document.write( "                             of the length 8 is  62*61*60*59*58*57*56*55   (6)\r\n" );
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document.write( "                             of the length 6, or 7 or 8 is the sum of number (4), (5) and (6).\r\n" );
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document.write( "(c)  To solve (c), subtract from N(a) the number of all possible passwords that do not have \r\n" );
document.write( "     digits in any position\r\n" );
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document.write( "        N(c) = N(a) -  =  - .\r\n" );
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