# Why do collisions in elementary reactions of higher-orders appear to be more likely?

So we are told that a unimolecular elementary reaction has a rate law of $k[\text{A}]$ where a termolecular reaction with three unique reagents, $A$, $B$ and $C$ has a rate law of $k[\text{A}][\text{B}][\text{C}]$. Now, other things being equal, and assuming for the sake of argument that the initial concentrations are all greater than 1M, this means that the termolecular elementary reaction is more likely at the outset. But that doesn't make much sense. There may be some statistical mechanics principle that's lost on me but it seems more likely that A bumps into A than, A, B and C come together all at once. So I don't quite follow this reasoning. Is it the case that $k$ is generally quite smaller in these termolecular elementary reactions?