Answer
The value of the given binomial coefficient is 4005.
Work Step by Step
Let us consider the provided expression, $\begin{align}
& \left( \begin{matrix}
90 \\
2 \\
\end{matrix} \right)=\frac{90!}{2!\left( 90-2 \right)!} \\
& =\frac{90!}{88!2!} \\
& =\frac{90\cdot 89}{2\cdot 1} \\
& =4005
\end{align}$
