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Find the number of 10-digit numbers where the sum of the digits is 3.

 Jun 3, 2020
 #1
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In order for the sum to be 3, the digits you can have are 0, 1, and 2. Think about how many ways you can arrange them and how many combinations there are! 

 Jun 3, 2020
 #2
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One gets the impression that there are "millions" of them !! But, in fact there are ONLY 55 as follows:

 

1000000002 , 1000000011 , 1000000020 , 1000000101 , 1000000110 , 1000000200 , 1000001001 , 1000001010 , 1000001100 , 1000002000 , 1000010001 , 1000010010 , 1000010100 , 1000011000 , 1000020000 , 1000100001 , 1000100010 , 1000100100 , 1000101000 , 1000110000 , 1000200000 , 1001000001 , 1001000010 , 1001000100 , 1001001000 , 1001010000 , 1001100000 , 1002000000 , 1010000001 , 1010000010 , 1010000100 , 1010001000 , 1010010000 , 1010100000 , 1011000000 , 1020000000 , 1100000001 , 1100000010 , 1100000100 , 1100001000 , 1100010000 , 1100100000 , 1101000000 , 1110000000 , 1200000000 , 2000000001 , 2000000010 , 2000000100 , 2000001000 , 2000010000 , 2000100000 , 2001000000 , 2010000000 , 2100000000 , 3000000000 , Total =  55

 Jun 3, 2020

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