**Core Concept**
The question tests the understanding of a specific tumor associated with a triad of symptoms, including diabetes, gallstones, and steatorrhoea. This combination of symptoms suggests an underlying pancreatic or ampullary pathology.

**Why the Correct Answer is Right**
The correct tumor associated with this triad is a somatostatinoma, a rare pancreatic or duodenal tumor secreting somatostatin. Somatostatin inhibits the release of various hormones, including insulin, leading to diabetes. It also inhibits cholecystokinin, leading to gallstones due to decreased gallbladder contraction, and inhibits pancreatic enzyme secretion, resulting in steatorrhoea.

**Why Each Wrong Option is Incorrect**
**Option A:** Not specified, but typically, other options like insulinoma or gastrinoma do not cause this specific triad.
**Option B:** Similarly, not specified, but it's unlikely to be the correct answer as the symptoms do not align with those of a typical glucagonoma or VIPoma.
**Option D:** Not provided, but it's not a somatostatinoma, which is the key tumor associated with the given symptoms.

**Clinical Pearl / High-Yield Fact**
Somatostatinomas are rare but notable for their association with this distinct triad of diabetes, gallstones, and steatorrhoea, making them a classic example in medical exams.

**Correct Answer:** D. Somatostatinoma.