A carry occurs when the place values have a sum ≥10.
For the 1's digit, there are 7 choices (0,1,2,3,4,5,6)
For the 10's digit, there are 4 choices (0,1,2,3)
For the 100's digit, there are 5 choices (1,2,3,4,5). Remember, we can't use 0 for the hundred's digit, because then the number wouldn't be 3-digits.
This means that there are 7×4×5 numbers. Thus, the answer is 140
.