How many tautologies are there? Given $m, n, k$, how many of $k$-DNFs with $n$ variables and $m$ clauses are tautology? (or how many $k$-CNFs are unsatisfiable?)
The answer depends on $k$, $m$, and $n$. Exact counts are generally not known, but there is a "threshold" phenomenon that for most settings of $k$, $m$, $n$, either nearly all $k$-SAT instances are satisfiable, or nearly all instances are unsatisfiable. For example, when $k=3$, it has been empirically observed that when $m &lt; 4.27 n$, all but a $o(1)$ fraction of 3-SAT instances are satisfiable, and when $m &gt; 4.27n$, all but a $o(1)$ fraction are unsatisfiable. (There are also rigorous proofs of bounds known.) 

One starting point is "The Asymptotic Order of the k-SAT Threshold". 

Amin Coja-Oghlan has also done a lot of work on these satisfiability threshold problems.