Evaluate Binomial Coefficient with Equal n and r

Evaluate the binomial coefficient when $n$ and $r$ are the same, for example, $\binom{9}{9}$.

The problem of evaluating the binomial coefficient when n and r are the same is a fundamental concept in combinatorics. The binomial coefficient, often denoted as C(n, r) or n choose r, represents the number of ways to choose r elements from a set of n elements without regard to the order of selection. A key property of binomial coefficients is that when n and r are equal, the binomial coefficient simplifies to 1. This is because there is exactly one way to choose all n elements from a set of n elements.