Find the number of solutions of `x + y + z + w = 20` under the following conditions:

Explanation

To find the number of solutions to the equation \( x + y + z + w = 20 \) under the condition that \( x, y, z, w > 0 \), we can follow these steps:

### Step 1: Transform the variables
Since \( x, y, z, w \) must be greater than zero, we can make a substitution to convert the problem into one where the variables can be zero. Let:
- \( x' = x - 1 \)
- \( y' = y - 1 \)
- \( z' = z - 1 \)
- \( w' = w - 1 \)
...