**Core Concept**
The question is testing the relative frequency of joint involvement in different types of arthritis, specifically focusing on the joints of the hand. This requires an understanding of the characteristic features and clinical presentations of various arthritic conditions.

**Why the Correct Answer is Right**
The correct answer is **Ankylosing Spondylitis (AS)**. AS is a type of seronegative spondyloarthropathy that primarily affects the axial skeleton, including the spine, sacroiliac joints, and costovertebral joints. The involvement of the peripheral joints, particularly those of the hand, is relatively uncommon in AS. In fact, the Modified New York criteria for diagnosing AS specify that peripheral joint involvement should not be a major criterion.

**Why Each Wrong Option is Incorrect**
* **Option A:** Rheumatoid Arthritis (RA) - RA is a classic example of an autoimmune arthritis that frequently involves the peripheral joints, including those of the hand. The involvement of the hands is a hallmark of RA, with symptoms such as pain, stiffness, and swelling in the hands and wrists.
* **Option B:** Psoriatic Arthritis (PsA) - PsA is another seronegative spondyloarthropathy that can involve both the axial and peripheral joints. The hands are commonly affected in PsA, with symptoms such as dactylitis (sausage-like swelling of the fingers) and enthesitis (inflammation of the tendons and ligaments).
* **Option D:** Gout - Gout is a type of inflammatory arthritis that typically presents with acute, episodic attacks of pain and swelling in the joints, particularly the base of the big toe. While gout can involve any joint, the hands are not a common site of involvement.

**Clinical Pearl / High-Yield Fact**
In clinical practice, it's essential to remember that the pattern of joint involvement can help differentiate between various arthritic conditions. For example, the presence of symmetrical joint involvement, particularly in the hands and feet, is more characteristic of RA, whereas the presence of asymmetric joint involvement, particularly in the lower limbs, is more characteristic of PsA.

**Correct Answer:** C. Ankylosing Spondylitis.