Variation of MAX 3-SAT

Question

Suppose we are given a 3CNF, and we want to know whether k clauses from this 3CNF can be satisfied (k being any natural number)?

I'm trying to think of an efficient algorithm to solve this problem. This is sort of a variation of the MAX 3-SAT, but with a fixed k. If we have m clauses, checking naively would get $\binom{m}{k}$ comparisons, but this seems factorial (if we approximate with Sterling's formula, exponential) complexity.

What could be an efficient way to check this? I must be missing something. Thanks.