The probability of a die rolling a given number at least $x$ times over the course of $n$ rolls

Say you have a $2000$-sided die, which you roll $2000$ times. I know the probability that you will get any given number (let's just say $1$) at least once in those $2000$ rolls is $1-.9995^{2000}$, i.e., $63.22\text{%}$. But how do you find the probability that you will roll a $1$ at least twice during a series of $2000$ rolls?