Assume, as seems likely, in the 2024 presidential election, Californians will cast 20 million votes. Make the simplifying assumption that that each Californian will vote Democrat with a probability of 60% (as they did in 2020).
What are the odds that California will tie exactly? It is given by the formula $$ f(k,n,p) = \mathbb{P}[X=k] = \binom{n}{k} p^k (1-p)^{n-k}. $$
$p = 0.6$, but unfortunately $n = 20,000,000$ and $k= 10,000,000$.
I know the value is “astronomical”, but I am trying to approximate it and am out of my depth. Trying to use Stirling’s approximation, I get $0.48^{30,000,000}/\pi$, but I have no confidence in that.