document.write( "Question 917724: Find the sum of all four digit numbers that can be formed using the digits 0,1,2,3,4, each digit appearing at most once \n" ); document.write( "

Algebra.Com's Answer #556784 by KMST(5328) $\"\"$ $\"About$

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There are 5 possible choices for the each of the last 3 digits.
\n" ); document.write( "The first digit cannot be 0, so there are only 4 choices for the first digit.
\n" ); document.write( "That gives us a total of $\"4%2A5%2A5%2A5=500\"$ numbers.
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\n" ); document.write( "The average of the unit digits is $\"%280%2B1%2B2%2B3%2B4%29%2F5=10%2F5=2\"$ .
\n" ); document.write( "So the sum of all the unit digits is $\"500%2A2=1000\"$
\n" ); document.write( "The same goes for the tens digits and the hundreds digits,
\n" ); document.write( "so the sum of all tens digits is 1000, for a sum value of 10,000,
\n" ); document.write( "and the sum of all hundreds digits is 1000, for a sum value of 100,000
\n" ); document.write( "The average of the first digits is $\"%281%2B2%2B3%2B4%29%2F4=10%2F4=2.5\"$ .
\n" ); document.write( "So the sum of all the first digits in all those 500 numbers must be
\n" ); document.write( " $\"500%2A2.5=1250\"$ .
\n" ); document.write( "The value of that sum is (1000)(1250)=1,250,000.
\n" ); document.write( "The value of the sum of all 500 numbers is
\n" ); document.write( "1,250,000+100,000+10,000+1000=1,361,000.\r
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