**Core Concept**
Pseudomonas aeruginosa is a Gram-negative bacterium that is inherently resistant to many antibiotics due to its unique cell wall structure and efflux pumps. Effective treatment of Pseudomonas infections requires antibiotics that can penetrate the outer membrane of the bacterium and target its cellular processes.

**Why the Correct Answer is Right**
Colistin is a polymyxin antibiotic that is effective against Pseudomonas aeruginosa. It works by binding to the lipopolysaccharide layer of the bacterial outer membrane, disrupting its structure and causing cell lysis. Colistin also acts by inhibiting the bacterial cell membrane's ability to maintain its potential, ultimately leading to cell death. Colistin's effectiveness against Pseudomonas is attributed to its ability to bypass the efflux pumps and penetrate the bacterial outer membrane.

**Why Each Wrong Option is Incorrect**
**Option A:** Ampicillin is a beta-lactam antibiotic that is primarily effective against Gram-positive bacteria and some Gram-negative bacteria, but it is not effective against Pseudomonas aeruginosa due to its resistance mechanisms.

**Option B:** Ceftriaxone is a third-generation cephalosporin antibiotic that is effective against a wide range of Gram-negative bacteria, but it is not effective against Pseudomonas aeruginosa due to its resistance to beta-lactam antibiotics.

**Option D:** Cefixime is a third-generation cephalosporin antibiotic that is effective against a wide range of Gram-negative bacteria, but it is not effective against Pseudomonas aeruginosa due to its resistance to beta-lactam antibiotics.

**Clinical Pearl / High-Yield Fact**
Polymyxin antibiotics like colistin are often used as a last resort for treating Pseudomonas infections due to their potential nephrotoxicity and neurotoxicity. However, their effectiveness against Pseudomonas makes them a crucial option in the treatment of severe infections.

**✓ Correct Answer: C. Colistin**