Let $n\geq 2$ be an integer and consider an array composed of $n$ rows and $2n$ columns. Half of the elements in the array are colored in red. Prove that for each integer $k$, 1$k$ rows such that the array of size $k\times 2n$ formed with these $k$ rows has at least $$\frac { k! (n-2k+2) } {(n-k+1)(n-k+2)\cdots (n-1)}$$ columns which contain only red cells.