The sum of the digits of a five-digit positive integer is 2 . (A five-digit integer cannot start with zero.) The number of such integers is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
The sum of the digits of a five-digit positive integer is 2 . (A five-digit integer cannot start with zero.) The number of such integers is
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

## Solution

If the sum of the digits of a five-digit positive integer is 2 , then the only possible integers are $20000,11000,10$ 100, 10 010, and 10001 . There are 5 such integers.