Moderate# Divisibility of Factorials and Binomial Coefficients by 499

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Which of the following numbers is divisible by the prime number $499$?

*A calculator is not needed.*

The notation $n!$ means *$n$ factorial*, defined as the product $1.2.\ldots.(n-1).n$ of all integers from $1$ to $n$.

The notation ${a\choose b}$, $1\le b\le a-1$, means the binomial coefficient ${a\choose b}=\cfrac{a!}{b!(a-b)!}$).

Select **ALL** that apply.