Consider a binary grid of size $4\times 4$, each of cell can either have $0$ or $1$. Among all possible $2^{16}$ arrangement how many arrangement of such grid exist in which each row and column contains even number of $1$s.
Solution which I thought
There will be $2$ possibilities for the answer of this question $1$st all ones in the $4\times 4$ grid that will count up to $1$ possible arrangement and $2$nd possibility will be $2$ ones in each row and column so how can i find the possible arrangement which will have $2$ ones in each row and column.
Am I right?