Find the number of non-negative intergral solutions of `x_(1)+x_(2)+x_(3)+x_(4)=20`.

Explanation

To find the number of non-negative integral solutions of the equation \( x_1 + x_2 + x_3 + x_4 = 20 \), we can use the combinatorial method known as "stars and bars."

### Step-by-Step Solution:

1. **Identify the Variables and Constants**:
We have the equation \( x_1 + x_2 + x_3 + x_4 = 20 \). Here, \( n = 20 \) (the total sum) and \( r = 4 \) (the number of variables).

2. **Use the Stars and Bars Theorem**:
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