Choose the correct definition of $\left(\begin{array}{l}n \\ k\end{array}\right)$ from below. A. $\frac{n !}{k !(n-k) !}$ B. $\frac{n !}{k !(k-n) !}$ C. $\frac{n !}{(n-k) !}$ D. $\frac{k !}{n !(n-k) !}$

Step 1 ：The symbol \(\begin{array}{l}n \\ k\end{array}\) represents a binomial coefficient, which is a key component in the binomial theorem. It is defined as the number of ways to choose k elements from a set of n elements, without regard to the order of selection.

Step 2 ：The correct formula for a binomial coefficient is \(\frac{n !}{k !(n-k) !}\), where n! denotes the factorial of n, k! denotes the factorial of k, and (n-k)! denotes the factorial of the difference between n and k.

Step 3 ：Final Answer: The correct definition of \(\begin{array}{l}n \\ k\end{array}\) is \(\boxed{A. \frac{n !}{k !(n-k) !}}\).