How many different positive integers exist between 10^9 and 10^10, the sum of whose digits is equal to 2?	Select the correct option:
A) 6  B) 7  C) 5  D) 8  E) 10
So, the numbers should be from 1,000,000,000 to 10,000,000,000   The following two cases are possible for the sum of the digits to be 2:   1. Two 1's and the rest are 0's:   1,000,000,001   1,000,000,010   1,000,000,100   1,000,001,000   1,000,010,000   1,000,100,000   1,001,000,000   1,010,000,000   1,100,000,000   9 numbers.   2. One 2 and the rest are 0's:   2,000,000,000   1 number.   Total = 10 numbers.   Answer: 10
<result>E</result>
How many different positive integers exist between 10^9 and 10^10, the sum of whose digits is equal to 2?