document.write( "Question 1160695: A briefcase lock opens with the correct 4-digit code. If the digits can be any number from 0-9 with no repetition, how many 4-digit codes are possible that end in a multiple of 3? \n" ); document.write( "

Algebra.Com's Answer #784070 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "So, there are 4 possibilities for the last digit in the 4-th position reading from left to right.\r\n" );
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document.write( "    These possibilities are 0, 3, 6 and 9.\r\n" );
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document.write( "Then there are 10-1 = 9 possibilities for the digit in  the 3-rd position;\r\n" );
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document.write( "                      8 possibilities for the digit in  the 2-nd position;\r\n" );
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document.write( "                      7 possibilities for the digit in  the 1-st position.\r\n" );
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document.write( "In all, there are  4*9*8*7 = 2016 different codes, satisfying imposed conditions.\r\n" );
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