Find the following sums :
(i) `sumsum_(inej) ""^(n)C_(i).""^(n)C_(j)` , (ii) `sumsum_(0leiltjlen) ""^(n)C_(i).""^(n)C_(j)`.
(iii) `sumsum_(0leiltjlen) ""^(n)C_(i).""^(n)C_(j)`.

Explanation

To solve the given sums, we will use the properties of binomial coefficients and some algebraic manipulations. Let's break down each part step by step.

### (i) Find the sum \( \sum_{i=0}^{n} \sum_{j=0}^{n} \binom{n}{i} \binom{n}{j} \)

1. **Understanding the Double Summation**:
The expression \( \sum_{i=0}^{n} \sum_{j=0}^{n} \binom{n}{i} \binom{n}{j} \) can be interpreted as the product of two sums:
\[
\left( \sum_{i=0}^{n} \binom{n}{i} \right) \left( \sum_{j=0}^{n} \binom{n}{j} \right)
...