How many different positive integers exist between 10^4 and 10^5, the sum of whose digits is equal to 2? Choose the correct answer:  A) 6  B) 7  C) 5  D) 8  E) 18
So, the numbers should be from 10,000 to 100,000   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:   10,001   10,010   10,100   11,000   4 numbers.   2. One 2 and the rest are 0's:   20,000   1 number.   Total = 5 numbers.   Answer: 5
<result>C</result>
How many different positive integers exist between 10^4 and 10^5, the sum of whose digits is equal to 2?