To solve the question regarding erythroblastosis fetalis and the conditions under which it can occur based on the blood groups of the parents, we will analyze each option step by step.
### Step 1: Understand Erythroblastosis Fetalis
Erythroblastosis fetalis is a condition that arises when there is an incompatibility between the blood types of the mother and the fetus, particularly concerning the Rh factor. This condition typically occurs when an Rh-negative mother carries an Rh-positive fetus, leading to the mother's immune system attacking the fetal red blood cells.
### Step 2: Analyze Each Option
1. **Mother: Rh-negative, Father: Rh-positive**
- In this scenario, there is a risk of erythroblastosis fetalis. If the fetus inherits the Rh-positive factor from the father, the mother’s immune system may produce antibodies against the Rh-positive blood cells, leading to the condition.
2. **Mother: Rh-negative, Father: Rh-negative**
- Here, both parents are Rh-negative. Therefore, all offspring will also be Rh-negative. There is no possibility of Rh incompatibility, and thus erythroblastosis fetalis cannot occur.
3. **Mother: Rh-positive, Father: Rh-negative**
- In this case, the mother is Rh-positive, meaning she does not have the antibodies against Rh-positive blood. Therefore, there is no risk of erythroblastosis fetalis, regardless of the father's blood type.
4. **Mother: Rh-positive, Father: Rh-positive**
- Similar to the previous case, both parents are Rh-positive. All offspring will also be Rh-positive, eliminating any risk of Rh incompatibility and erythroblastosis fetalis.
### Step 3: Conclusion
Based on the analysis:
- Erythroblastosis fetalis can occur in the first scenario (Rh-negative mother and Rh-positive father).
- It cannot occur in the second (both parents Rh-negative), third (Rh-positive mother and Rh-negative father), and fourth (both parents Rh-positive) scenarios.
Thus, the answer to the question is that erythroblastosis fetalis can never occur in children born to parents with the following blood groups: **II, III, and IV**.
### Final Answer
**The correct options are II, III, and IV.**
