# filling up numbers in a matrix

Suppose you have a $k.n \times 2$ matrix. You have to fill up the numbers $1,2,3, \cdots, n$ as entries in such a way that in each column it is non-decreasing, in each row it is strictly increasing and each number should appear exactly $2k$ times. How many ways one can fill up the matrix ?

• No, it is possible. For example take $k=1$ and $n=5$. Then the rows of the matrix are $(1,2),(1,2),(3,4),(3,5),(4,5)$. – Harry Feb 11 '15 at 14:09