Evaluate the binomial coefficient.
\[
\left(\begin{array}{l}
13 \\
10
\end{array}\right)
\]

Step 1 ：We are given the binomial coefficient to evaluate as \(\begin{array}{l} 13 \\ 10 \end{array}\)

Step 2 ：The binomial coefficient is calculated using the formula: \(\begin{array}{l} n \\ k \end{array} = \frac{n!}{k!(n-k)!}\) where 'n!' denotes the factorial of n, which is the product of all positive integers less than or equal to n.

Step 3 ：In this case, n = 13 and k = 10. So, we need to calculate: \(\begin{array}{l} 13 \\ 10 \end{array} = \frac{13!}{10!(13-10)!}\)

Step 4 ：By calculating the above expression, we find that the binomial coefficient is 286.0

Step 5 ：Final Answer: The binomial coefficient is \(\boxed{286}\)