**Core Concept**
The Bismuth-Corlette classification system is a widely used classification system for hilar cholangiocarcinomas, which helps in determining the extent of tumor spread and guiding treatment decisions. This classification system takes into account the location and extent of tumor involvement in the bile ducts.

**Why the Correct Answer is Right**
Perihilar cholangiocarcinomas extending into the right secondary intrahepatic ducts are classified as type III according to the Bismuth-Corlette classification system. This classification is based on the tumor's relationship with the confluence of the right and left hepatic ducts (Klatskin tumor) and the extent of tumor involvement in the bile ducts. Type III tumors involve the right secondary intrahepatic ducts and can be further subdivided into type IIIa (tumor extending into the right secondary intrahepatic ducts) and type IIIb (tumor extending into the left secondary intrahepatic ducts). The correct classification is essential for determining the appropriate treatment strategy, which may involve surgical resection, transplantation, or other modalities.

**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because it does not accurately describe the extent of tumor involvement in the bile ducts according to the Bismuth-Corlette classification system.
**Option B:** Incorrect because it is not a recognized classification for perihilar cholangiocarcinomas according to the Bismuth-Corlette system.
**Option D:** Incorrect because it is not a valid classification for perihilar cholangiocarcinomas extending into the right secondary intrahepatic ducts.

**Clinical Pearl / High-Yield Fact**
The Bismuth-Corlette classification system is a crucial tool for surgeons and oncologists to determine the extent of tumor spread and guide treatment decisions in patients with hilar cholangiocarcinomas. Understanding this classification system is essential for accurate staging and treatment planning.

**Correct Answer:** C.