Step 1: Understanding the Concept
All cells of the embryo sac arise by mitosis from the haploid functional megaspore.
Step 2: Match each structure
(A) Definitive nucleus: two polar nuclei fuse, so it is 2n (III).
(B) Synergid: it is haploid, n (I).
(C) Primary endosperm nucleus: formed by fusion of one male gamete (n) with the definitive nucleus (2n), so it is 3n (II).
Step 3: Conclusion
The pairs are (A)-(III), (B)-(I), (C)-(II).
Final Answer:
The matching is (A)-(III), (B)-(I), (C)-(II).
\[ \boxed{\text{(B) }\text{(A) - (III), (B) - (I), (C) - (II).}} \]