of specific medical conditions

[keannu]

I guess the reason why a can't be the answer is "with" is proper for the possessive meaning, while "of" can mean such type, but I want to be sure....

Q. Insurance providers often refuse to offer coverage to people ____c_______
a. of specific medical conditions
b.have specific conditions of medical
c.that have specific medical conditions.
d. having that specific conditions of medicine.

[Raymott]

I guess the reason why a. can't be the answer is that "with" is proper for the possessive meaning, while "of" can mean such type, but I want to be sure....
No, the reason that 'a' can't be the right answer has nothing to do with the meaning or usage of alternatives that aren't even there.
The reason that a. can't be the answer is that we don't say "people of a medical condition".
Q. Insurance providers often refuse to offer coverage to people ____c_______
a. of specific medical conditions
b.have specific conditions of medical
c.that have specific medical conditions.
d. having that specific conditions of medicine.

I would have written "people who have ..."