If m,n,r are positive integers such that r `lt ` m,n, then
`""^(m)C_(r)+""^(m)C_(r-1)""^(n)C_(1)+""^(m)C_(r-2)""^(n)C_(2)+...+ ""^(m)C_(1)""^(n)C_(r-1)+""^(n)C_(r)` equals

Explanation

To solve the given problem, we need to evaluate the expression:

\[ \binom{m}{r} + \binom{m}{r-1} \binom{n}{1} + \binom{m}{r-2} \binom{n}{2} + \ldots + \binom{m}{1} \binom{n}{r-1} + \binom{n}{r} \]

### Step 1: Understand the Binomial Coefficient
The binomial coefficient \(\binom{m}{k}\) represents the number of ways to choose \(k\) elements from a set of \(m\) elements. We will use the properties of binomial coefficients and the binomial theorem to simplify the expression.
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