The number of integral solutions of equation `x+y+z+t=29,` when `x >= 1, y >= 2, z>=2, 3 and t >= 0` is

Explanation

To find the number of integral solutions of the equation \( x + y + z + t = 29 \) under the conditions \( x \geq 1 \), \( y \geq 2 \), \( z \geq 3 \), and \( t \geq 0 \), we can follow these steps:

### Step 1: Adjust the variables
First, we need to account for the minimum values of \( x \), \( y \), and \( z \). We can do this by substituting new variables:
- Let \( x' = x - 1 \) (so \( x' \geq 0 \))
- Let \( y' = y - 2 \) (so \( y' \geq 0 \))
- Let \( z' = z - 3 \) (so \( z' \geq 0 \))
- \( t \) remains as it is since \( t \geq 0 \)
...