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For problem 11b, which asks how many different routes there are from point A to point B if you travel only north or west, we can solve this by calculating the number of paths using combinatorics.

### Step-by-Step Solution:

1. **Determine the grid dimensions**:
   From the image, point A is at the bottom-right and point B is at the top-left of a \(4 \times 4\) grid. This means you need to travel 4 units north and 4 units west.

2. **Understanding the problem**:
   Since you can only move north or west, a total of 8 moves are required:
   - 4 moves north (N) 
   - 4 moves west (W)

3. **Using combinations**:
   The number of distinct routes is equivalent to the number of ways to arrange 4 north moves and 4 west moves in a sequence of 8 moves. This is a combinations problem, calculated as:
   \[
   \binom{8}{4} = \frac{8!}{4!4!}
   \]

4. **Calculation**:
   \[
   \binom{8}{4} = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} = 70
   \]

Thus, there are **70 different routes** from A to B if you can only move north or west.

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Would you like further details on this calculation or have any questions? Here are some related questions to expand on this concept:

1. What if the grid was a \(5 \times 5\) grid? How many routes would there be?
2. How would the solution change if diagonal movements were allowed?
3. If one of the north or west moves was blocked by an obstacle, how would you calculate the new number of routes?
4. How do you solve this using Pascal’s Triangle?
5. What if you could take a shortcut, skipping one block—how would that affect the total number of routes?

**Tip**: When solving combinatorial grid problems, always ensure you correctly identify the total number of moves and how many steps in each direction are needed.

Solve the combinatorics problem of finding the number of different routes from point A to B on a 4x4 grid, where movements are restricted to only north or west. Use the combination formula C(8,4) to find 70 different paths. Suitable for Grades 9-12.

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