Consider the equation `x_(1)+x_(2)+x_(3)`=10 , then
(i) Find the number of non-negative integral solution.
(ii) Find the positive integral solution.

Explanation

To solve the problem, we will break it down into two parts as given in the question.

### Part (i): Find the number of non-negative integral solutions to the equation \( x_1 + x_2 + x_3 = 10 \).

1. **Identify the values of \( n \) and \( r \)**:
- Here, \( n = 10 \) (the total sum we want) and \( r = 3 \) (the number of variables \( x_1, x_2, x_3 \)).

2. **Use the formula for non-negative integral solutions**:
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