**Core Concept**
The patient's symptoms suggest an acute abdomen with a palpable mass, indicating a possible intestinal obstruction or a mass-forming lesion in the gastrointestinal tract. The presence of blood and mucus in stool, along with abdominal pain, points towards a diagnosis of intussusception or a gastrointestinal malignancy.

**Why the Correct Answer is Right**
Intussusception occurs when a part of the intestine invaginates into another, leading to obstruction and potentially ischemia. The palpable mass is likely the intussuscepted segment, which may be a tumor, polyp, or other lesion. The blood and mucus in stool are due to mucosal ischemia and sloughing of the intussuscepted segment. The correct diagnosis of intussusception requires a high index of suspicion, as it is often a clinical diagnosis based on the patient's symptoms and signs.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because, although appendicitis can present with abdominal pain and a palpable mass, it does not typically cause blood and mucus in stool.

**Option B:** This option is incorrect because, although a gastrointestinal malignancy can cause a palpable mass and blood in stool, it is less likely to cause mucus in stool and intussusception is a more specific diagnosis in this context.

**Option C:** This option is incorrect because, although a Meckel's diverticulum can cause gastrointestinal bleeding, it is less likely to cause a palpable mass and mucus in stool.

**Clinical Pearl / High-Yield Fact**
Intussusception is a classic example of a "lead point" causing a palpable mass, and it is essential to consider this diagnosis in any patient presenting with abdominal pain, blood and mucus in stool, and a palpable mass.

**Correct Answer:** C.