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To solve this problem, we need to determine the number of ways a person can walk from point A to point C, passing through point B, while only moving rightwards or upwards. The grid shown is a 5x5 grid, with points A, B, and C located as follows:

- \( A \) is at the bottom-left corner (0, 0).
- \( B \) is at the center (3, 2).
- \( C \) is at the top-right corner (5, 5).

### Steps:

1. **From A to B:**
   - To move from \( A(0, 0) \) to \( B(3, 2) \), the person needs to make exactly 3 rightward moves and 2 upward moves.
   - The number of ways to arrange these 3 rightward and 2 upward moves is given by the number of permutations of these 5 moves (3 rightward, 2 upward):
     \[
     \binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{5 \times 4}{2 \times 1} = 10
     \]
   So, there are 10 ways to go from A to B.

2. **From B to C:**
   - To move from \( B(3, 2) \) to \( C(5, 5) \), the person needs to make exactly 2 rightward moves and 3 upward moves.
   - The number of ways to arrange these 2 rightward and 3 upward moves is given by the number of permutations of these 5 moves (2 rightward, 3 upward):
     \[
     \binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{5 \times 4}{2 \times 1} = 10
     \]
   So, there are 10 ways to go from B to C.

### Total Number of Ways:
Since the two parts (A to B and B to C) are independent, the total number of ways is the product of the two:
\[
10 \times 10 = 100
\]

### Final Answer: 
There are **100 ways** to walk from A to C via B.

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Do you want more details on any of the steps? Feel free to ask!

Here are five related questions to explore further:

1. How do you calculate the number of combinations for any two points on a grid?
2. What if diagonal movements were allowed? How would that change the calculation?
3. What if the grid was larger (e.g., 7x7)? How would you calculate the number of ways from A to C via B?
4. How does the problem change if obstacles are placed on the grid?
5. How would you calculate the shortest path if the grid was not square?

**Tip:** The number of ways to move in a grid is typically based on choosing how many moves to make in each direction, often calculated with combinations (binomial coefficients).

In the figure, in how many ways can a person walk from A to C via B, if he walks either rightwards or upwards?

Learn how to calculate the number of ways a person can walk from point A to point C on a 5x5 grid while passing through point B. This problem covers combinatorics and grid movement using the combination formula and binomial coefficient theorem. Suitable for students in Grades 9-12.

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