### Core Concept
The newborn baby's presentation with profuse bleeding from the umbilical stump suggests a disorder of hemostasis, specifically a problem with platelet function or number. This condition is known as bleeding disorder or coagulopathy.

### Why the Correct Answer is Right
The correct answer is likely due to a deficiency of von Willebrand factor (vWF), a protein essential for platelet adhesion and aggregation at sites of vascular injury. vWF also serves as a carrier protein for factor VIII, protecting it from degradation. In the absence of vWF, factor VIII levels may be normal, but its activity may be impaired. This condition is known as von Willebrand disease (vWD), the most common inherited bleeding disorder.

### Why Each Wrong Option is Incorrect
**Option A:** This option is incorrect because the patient's PT and APTT are within normal limits, which suggests that the coagulation cascade is intact and the bleeding disorder is not due to a deficiency of coagulation factors such as fibrinogen, prothrombin, or factors II, V, VII, or X.

**Option B:** This option is incorrect because the patient's presentation is not consistent with hemophilia A, which is caused by a deficiency of factor VIII. While hemophilia A can present with bleeding from the umbilical stump, the patient's normal PT and APTT suggest that the coagulation cascade is intact.

### Clinical Pearl / High-Yield Fact
The umbilical stump is a common site for bleeding in newborns with von Willebrand disease, as it is a site of vascular injury that requires platelet adhesion and aggregation to stop bleeding.

### Correct Answer: C. von Willebrand disease.