Explanation:

- Infirmary:

- This is a place in a large institution for caring for those who are ill. It is often found in schools, military bases, and other establishments, making it the right choice for the given description.

- Hostel:

- Typically refers to budget accommodations for travelers, not specifically for caring for the ill. It's more like a shared lodging space.

- Hangar:

- A large building for storing aircraft. Not related to healthcare or caring for the ill.

- Dormitory:

- A room or building with sleeping quarters, primarily used in schools or colleges for student accommodations. It is not meant for medical care.