(Solved): Problem 2. Consider the grid of points shown below. Starting at the point labelled \( A \), you ca ...

Problem 2. Consider the grid of points shown below. Starting at the point labelled \( A \), you can go one step up or one step right at each move. This is repeated until the point labelled \( B \) is reached. How many paths are there from \( A \) to \( B \) that go through the point circled? (Hint: call the point \( P \), and count the paths from \( A \) to \( P \) and \( P \) to \( B . \) )