Expected number of four-card subsets from a Poisson box

A box contains $N\sim\text{Poisson}(6)$ cards. Someone will pick a set of $4$ of them. What is the expected number of different 4-card sets that can be picked, i.e. $\mathbb{E}\big[\binom N4\big]$ (with $\binom nk=0$ when $n<k$)?

$54$. $\binom N4=\tfrac{N(N-1)(N-2)(N-3)}{4!}$, and the falling factorial moments of a Poisson($\lambda$) are $\lambda^k$. So the expectation is $\tfrac{6^4}{24}=54$.