**Core Concept**
Osteomas, adenomatous polyps of the intestine, and periampullary carcinomas are characteristic manifestations of a rare genetic disorder. This condition is caused by mutations in a specific gene involved in cell growth regulation.

**Why the Correct Answer is Right**
The correct answer is associated with Familial Adenomatous Polyposis (FAP), a hereditary condition characterized by the development of multiple adenomatous polyps in the colon and rectum. These polyps have a high risk of progressing to colorectal cancer if left untreated. Osteomas, a type of benign bone tumor, and periampullary carcinomas, a type of cancer near the ampulla of Vater, are also associated with FAP. The genetic mutation underlying FAP leads to the activation of the Wnt signaling pathway, promoting uncontrolled cell growth and tumor formation.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because Turcot syndrome is a different genetic disorder characterized by the combination of colorectal polyposis and central nervous system tumors, such as medulloblastoma.
* **Option B:** This option is incorrect because Peutz-Jeghers syndrome is a distinct genetic disorder characterized by the development of hamartomatous polyps in the gastrointestinal tract and an increased risk of certain cancers, but it is not typically associated with osteomas or periampullary carcinomas.
* **Option C:** This option is incorrect because Gorlin syndrome is a genetic disorder characterized by the development of basal cell carcinomas, jaw keratocysts, and other abnormalities, but it is not typically associated with adenomatous polyps or periampullary carcinomas.

**Clinical Pearl / High-Yield Fact**
FAP is an autosomal dominant disorder, meaning that a single copy of the mutated gene is sufficient to cause the condition. Patients with FAP have a nearly 100% risk of developing colorectal cancer if left untreated, highlighting the importance of early detection and treatment.

**Correct Answer: C. Gardner syndrome**