document.write( "Question 889798: Among the 8! permutations of the digits 1,2,,,,,8 consider those arrangements which have the following property if you take any 5 consecutive ppositions the product of the digits in those positions is divisible by 5.the number of such aarrangements is
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Algebra.Com's Answer #538502 by Edwin McCravy(20063)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "It's not any of those answers.\r\n" );
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document.write( " 1 2 3 4 5 6 7 8\r\n" );
document.write( " X X X X X _ _ _  <- the product of the digits where the X's are must have a 5.\r\n" );
document.write( " _ X X X X X _ _  <- the product of the digits where the X's are must have a 5.    \r\n" );
document.write( " _ _ X X X X X _  <- the product of the digits where the X's are must have a 5.\r\n" );
document.write( " _ _ _ X X X X X  <- the product of the digits where the X's are must have a 5.\r\n" );
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document.write( "The only one of the digits 1-8 that can cause a product\r\n" );
document.write( "to be divisible by 5 is the number 5 itself.  So the 5 \r\n" );
document.write( "must be in position 4 or 5 in order for you to be \r\n" );
document.write( "able to take any 5 consecutive positions and the product \r\n" );
document.write( "of the digits in those positions will be divisible by 5.  \r\n" );
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document.write( "So \r\n" );
document.write( "We can choose the position for the 5 in any of 2 ways.\r\n" );
document.write( "We can choose the position for the 1 in any of the 7 remaining ways.\r\n" );
document.write( "We can choose the position for the 2 in any of the 6 remaining ways.\r\n" );
document.write( "We can choose the position for the 3 in any of the 5 remaining ways.\r\n" );
document.write( "We can choose the position for the 4 in any of the 4 remaining ways.\r\n" );
document.write( "We can choose the position for the 6 in any of the 3 remaining ways.\r\n" );
document.write( "We can choose the position for the 7 in either of the 2 remaining ways.\r\n" );
document.write( "We can choose the position for the 8 only the 1 remaining way.\r\n" );
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document.write( "Answer 2×7×6×5×4×3×2×1 2×7! = 10080.\r\n" );
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document.write( "Edwin
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