The text in the image describes a problem where a frog starts at the origin (0, 0) in a coordinate plane. From any point $(x, y)$, the frog can jump to one of the following points:

• $(x+2, y)$
• $(x+3, y)$
• $(x, y+3)$

The problem asks how many different sequences of jumps the frog can take to move from point $(0,0)$ to point $(6,5)$.

Let’s analyze this step by step:

1. Goal: The frog needs to reach point $(6,5)$.

   • It needs to make exactly $6$ units of movement in the x-direction.
   • It needs to make exactly $5$ units of movement in the y-direction.

2. X-direction moves: The frog can either jump by 2 or by 3 units in the x-direction, so we need to find all combinations of these moves that sum up to 6.

   • Possible combinations of moves:
     • 3 jumps of 2 units (3x2 = 6)
     • 2 jumps of 3 units (2x3 = 6)
     • 1 jump of 2 units and 1 jump of 3 units (2 + 3 + 1 = 6)

3. Y-direction moves: The frog can only jump by 3 units in the y-direction. So there