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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

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), or (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).

Explore how to calculate the number of distinct jump sequences a frog can take on a coordinate plane to reach from point (0,0) to (6,5). This problem involves combinatorics and coordinate geometry to determine all possible paths using specific jumps.

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