Final answer:
The eligible groups for selection into the study are children receiving x-rays in 1990, children receiving x-rays for broken bones in 1983, and children in the hospital for cancer treatment in 1985.
Step-by-step explanation:
In this retrospective cohort study, the eligible groups for selection into the study are:
- Children receiving x-rays in 1990
- Children receiving x-rays for broken bones in 1983
- Children in the hospital for cancer treatment in 1985
These groups are eligible because the study was done using records from 1980 to 1985, so children receiving x-rays in 1990 and children treated in private clinics and hospitals in 1981 are not within the study period. Children receiving x-rays in 1975 are also not eligible as they are outside the study period.