To solve the seating arrangement problem, let's break it down step by step.
### Step 1: Understanding the Information
We have seven people: A, B, C, D, E, F, and G. Five of them are facing the center, and two are facing away from the center.
### Step 2: Placing C and D
- It is given that C sits third to the left of D and both are facing the center.
- Let's place D at position 1. Therefore, C will be at position 4 (since left means counter-clockwise).
```
Position: 1 (D) - 2 - 3 - 4 (C) - 5 - 6 - 7
```
### Step 3: Placing E
- E is neither an immediate neighbor of D nor of C. Therefore, E cannot be in positions 2, 3, or 5. The only position left for E is position 6.
```
Position: 1 (D) - 2 - 3 - 4 (C) - 5 - 6 (E) - 7
```
### Step 4: Placing F
- The person sitting exactly between D and F is facing opposite to the center. Since D is at position 1, the only position between D (1) and F can be position 2. Therefore, F must be at position 3 (facing the center).
```
Position: 1 (D) - 2 (X) - 3 (F) - 4 (C) - 5 - 6 (E) - 7
```
(Note: X represents a person facing away from the center.)
### Step 5: Placing G and A
- G sits third to the right of A and is facing the center.
- If we place A at position 5, then G will be at position 1 (but D is already there).
- If A is at position 6, G will be at position 2 (but E is already there).
- If A is at position 7, G will be at position 3 (but F is already there).
- The only valid position for A is position 2, making G at position 5.
```
Position: 1 (D) - 2 (A) - 3 (F) - 4 (C) - 5 (G) - 6 (E) - 7 (X)
```
### Step 6: Placing B
- We know that one of B's neighbors is facing opposite to the center. The only position left for B is position 7.
```
Position: 1 (D) - 2 (A) - 3 (F) - 4 (C) - 5 (G) - 6 (E) - 7 (B)
```
### Step 7: Final Arrangement
Now we have:
- D (1) - facing center
- A (2) - facing center
- F (3) - facing center
- C (4) - facing center
- G (5) - facing center
- E (6) - facing away from center
- B (7) - facing away from center
### Step 8: Finding the Position of F with respect to B
- From B's position (7), F is at position 3.
- To find F's position with respect to B, we count the positions:
- 1st to the left (6), 2nd to the left (5), 3rd to the left (4), and 4th to the left (3).
Thus, F is **4th to the left of B**.
### Conclusion
The position of F with respect to B is **4th to the left**.
