document.write( "Question 952916: how many 5 digit counting numbers contain at least one 6
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Algebra.Com's Answer #721003 by ikleyn(52780) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Step 1.\r
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document.write( "How many are there 5 digit counting numbers in all ?\r\n" );
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document.write( "The answer is  9*10*10*10*10 = 90000,  because such a number can have\r\n" );
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document.write( "    - any of  9 digits from 1 to 9 in the mostleft position;\r\n" );
document.write( "    - any of 10 digits from 0 to 9 in the 2nd position;\r\n" );
document.write( "    - any of 10 digits from 0 to 9 in the 3rd position;\r\n" );
document.write( "    - any of 10 digits from 0 to 9 in the 4th position;\r\n" );
document.write( "    - any of 10 digits from 0 to 9 in the 5th position.\r\n" );
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document.write( "In all, there are 90000 such numbers.\r\n" );
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document.write( "How many are there 5 digit counting numbers that HAVE NO the digit 6 ?\r\n" );
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document.write( "The answer is 8*9*9*9*9 = 52488, because such a number can have\r\n" );
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document.write( "    - any of  8 digits from 1 to 9 except of 6 in the mostleft position;\r\n" );
document.write( "    - any of  9 digits from 0 to 9 except of 6 in the 2nd position;\r\n" );
document.write( "    - any of  9 digits from 0 to 9 except of 6 in the 3rd position;\r\n" );
document.write( "    - any of  9 digits from 0 to 9 except of 6 in the 4th position;\r\n" );
document.write( "    - any of  9 digits from 0 to 9 except of 6 in the 5th position.\r\n" );
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document.write( "Now the number under the problem's question is the difference 90000 - 52488 = 37512.\r\n" );
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