Are you trying to sample the individual terms in the series? In other words, each term in the expansion looks like $(-1)^k\binom{100}{k}(10)^{n-k}(9)^k$ where you can temporarly drop the $(-1)^k$ to see that sampling a binomial distribution with $n=100$ and probability coefficient $p=10/19$ will give you want you want:
$P(B(n,p)=k)=\binom{100}{k}p^k(1-p)^{n-k}$
so
$(-1)^k\binom{100}{k}(10)^{n-k}(9)^k=(-1)^k\cdot 19^n\cdot P(B(n,p)=k)$
In other words, flip $n=100$ biased coins of probability $p=10/19$ and then count the number of heads that appear. Repeat over and over to get an approximation of the binomial distribution.