Nine persons – A, B, C, D, E, F, G, H, and I – are sitting around a circular table, all facing towards the center. But not necessarily in the same order.

Only one person sits between A and F. C sits third to the right B, who is an immediate neighbor of A. Only three people sit between A and G. G sits second to the left of H. I is an immediate neighbor of both A and H. F is not an immediate neighbor of D.

Who among the following sit between C and B when counted in clockwise direction from B?
I. H
II. F
III. D

To find the correct seating arrangement of the nine persons (A, B, C, D, E, F, G, H, and I) sitting around a circular table facing the center, we can trace the positions step-by-step. Let us assign positions 1 to 9 in a clockwise direction around the circular table.

Since everyone is facing the center:
- "Left" refers to the clockwise direction.
- "Right" refers to the counter-clockwise direction.

Step 1: Position A, I, and H
We are given that "I is an immediate neighbor of both A and H." This means the three must sit in the order A-I-H or H-I-A.
Let us place A at position 1 and I at position 2.
This forces H to be at position 3.

Step 2: Position G
We are given that "G sits second to the left of H."
Starting from H at position 3 and moving clockwise (left), the second position is position 5.
Therefore, G is at position 5.
We can verify that "only three people sit between A and G" along this path, which are the persons at positions 2 (I), 3 (H), and 4. This is consistent with the clues.

Step 3: Position B and C
We are given that "B is an immediate neighbor of A."
Since position 2 is already occupied by I, B must be at position 9 (the other neighbor of position 1).
Next, "C sits third to the right of B."
Starting from B at position 9 and moving counter-clockwise (right), the third position is position 6 (9 ⇒ 8 ⇒ 7 ⇒ 6).
Therefore, C is at position 6.

Step 4: Position F and D
We are given that "only one person sits between A and F."
A is at position 1. The positions with exactly one person in between are position 3 (occupied by H) and position 8.
Thus, F must sit at position 8.
We are also told that "F is not an immediate neighbor of D."
F is at position 8, so D cannot be at position 7. The only other available position for D is position 4.
Therefore, D is at position 4.
The remaining person, E, must occupy the last remaining position, which is position 7.

Summary of the Seating Arrangement:
Moving clockwise from 1 to 9:
- Position 1: A
- Position 2: I
- Position 3: H
- Position 4: D
- Position 5: G
- Position 6: C
- Position 7: E
- Position 8: F
- Position 9: B

Answering the Question:
We need to find who sits between C (position 6) and B (position 9) when counted in the clockwise direction from B.
Counting clockwise from B (position 9):
B (9) ⇒ A (1) ⇒ I (2) ⇒ H (3) ⇒ D (4) ⇒ G (5) ⇒ C (6)
The persons sitting between C and B in this direction are A, I, H, D, and G.
Checking the given options:
I. H (Sits between them)
II. F (Does not sit between them)
III. D (Sits between them)

Therefore, both I and III sit between C and B when counted clockwise from B.