Since the source was mentioned in the footer, you can Google HDU 5155 solution for some initial ideas. However, the given solutions are all too slow — ~\mathcal{O}(N^3)~ or ~\mathcal{O}(N^4)~. To speed it up, you can assume each row has at least one 1 (~(2^C-1)^R~ ways to do so) and either use the Inclusion-Exclusion Principle or dynamic programming with the binomial coefficient to compute the ways with ~R~ rows and ~i~ columns for ~1 \le i \le C~.

Time complexity: ~\mathcal{O}(C \log R)~ or ~\mathcal{O}(C^2 + C \log R)~