Hypergraph Intro

In mathematics, hypergraph is a generalization of a graph in which an edge can join any number of vertices (denoted as $m$), therefore introducing hyperedges.

In that case, the number of hyperedges of size $m$ that a complete hypergraph with $n$ many vertices has a more general formula, which boils down to well-know formula $\frac{n(n-1)}{2}$ for $m=2$.

Given that a complete hypergraph with $n=11$ number of vertices, it can be shown that the number of hyperedges of size $m=3$ is $165$. Then, what is the answer for $n=1007$ and $m=35$?

Note: This is rather an easy problem with an immediate solution, but serves as a conceptual introduction to prospective problems related to hypergraphs.