Select a subset of the columns in $2\times n$ matrix, is it easy?
Hint: Show that it is NP-hard by reduction from EQUAL-PARTITION, the variant of PARTITION in which we require both parts to have equal sizes (see a question on math.se).

Given an instance $\{x_1,\ldots,x_n\}$ of EQUAL-PARTITION (with $x_i &gt; 0$), consider an instance of your problem with $b = n/2$, $c = \sum_i (M+x_i)/2 - 1$ for large enough $M$ (I think that $M = \max_i x_i$ should suffice), and the matrix
$$
\begin{bmatrix}
M+x_1 &amp; \cdots &amp; M+x_n \\
M+\frac{\sum_i x_i}{n/2}-x_1 &amp; \cdots &amp; M+\frac{\sum_i x_i}{n/2}-x_n
\end{bmatrix}.
$$