Find the probability of occurrence of each edge in a graph having $n$ nodes after $k$ operations

Given a graph with $ n$ nodes . The adjacency matrix of the graph is given. We do $ k$ operations on this graph. In each operation we choose two distinct nodes $ i$ and $ j$ (there are $ (n*(n-1))/2$ such choices) equiprobably (all choices are equiprobable) and if there exists a edge between $ i$ and $ j$ we delete that edge or else we draw an edge between the chosen pair of nodes.
We have to output a $ n*n$ matrix where the element at $ (i,j)th$ position denotes the probability of occurrence of edge connecting the nodes $ i$ and $ j$ in the final resulting graph.
The constraints on n and k are $ n<=50$ and $ k<=50$ .
I tried it using dynamic programming but could figure out transitions properly.
Can you please help me out.