Total number of bit-strings that start with 3 ones and end with 2 ones

Question

I have a problem where I need to find the total number of bit-strings with the length of 30 that start with 3 ones and end with 2 ones. The total number of 1s in the string is 17 and the total number of 0s is 13. It would look something like this, with 25 empty spots in the middle of the bit-string:
1 1 1 _ ... _ 1 1
My initial guess for solving this is to find all possible combinations for the remaining empty spots in the bit strings with: $${25 \choose 12\quad 13} $$ I am not sure if this solution is correct or if I should apply the inclusion-exclusion principle. If I need to apply that principle, how would it be done?