(a) Any person entitled to administration may relinquish his or her right thereto in the same manner as executors are authorized to renounce their appointment.
(b) If no person entitled to the administration of the estate, according to the first three subdivisions of subsections (a) or (b) of Section 43-2-42, applies for letters within 40 days after the death of the intestate is known, the persons so entitled must be held to have relinquished their right to the administration.