Question 8
A frog is positioned at the origin in the coordinate plane. From the point $(x, y),$ the frog can jump to any of the points $(x + 1, y),$ $(x + 2, y),$ $(x, y + 1),$ or $(x, y + 2).$ Find the number of distinct sequences of jumps in which the frog begins at $(0, 0)$ and ends at $(4, 4).$