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This is a counting problem in which we are asked to determine how many paths exist from point \(A\) to point \(F\) following the direction of the arrows. The figure shows a directed graph with multiple points (A, B, C, D, E, F) and arrows indicating the direction of travel between the points.

To solve this, we can count the number of distinct paths by considering each possible route from \(A\) to \(F\).

1. **Path via \(B\):**
   - One direct path from \(A \to B \to F\). This gives us **1 path**.

2. **Path via \(C\):**
   - First, \(A \to B \to C\), then from \(C \to F\). So, \(A \to B \to C \to F\) is **1 path**.

3. **Path via \(E\):**
   - \(A \to E \to F\), a direct path. This gives **1 path**.

4. **Path via \(D\):**
   - \(A \to D \to E \to F\). This route contributes **1 path**.

5. **Additional paths via point \(E\):**
   - There is another path where \(A \to E \to F\) again contributes **1 path**, but it was already considered, so there are no new paths here.

### Total Paths:
Adding up all distinct paths:
- \(A \to B \to F = 1\)
- \(A \to B \to C \to F = 1\)
- \(A \to E \to F = 1\)
- \(A \to D \to E \to F = 1\)

The total is **4 paths**, which corresponds to option **(B) Four**.

Would you like more details, or have any questions?

Here are some related questions you can explore:
1. What is the method to count paths in more complex graphs?
2. How does a change in graph direction affect the number of paths?
3. How can you apply combinatorics in determining paths in non-directed graphs?
4. How does dynamic programming help in solving counting path problems?
5. What if there were cycles in the graph? How would that impact the number of paths?

**Tip:** When solving path-counting problems, ensure you account for all possible routes, and avoid double-counting paths by revisiting already explored ones.

In the figure shown, how many paths in the direction of the arrows exist from point A to point F?

Explore how to count the number of distinct paths from point A to point F in a directed graph. This problem utilizes key concepts from graph theory and path counting, suitable for high school students in Grades 9-12.

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