Coins Along the Diagonals

In a $4\times4$ grid of cells, coins are placed at random into $8$ of the $16$ cells so that there are $2$ coins in each row and $2$ coins in each column of the grid. The probability that all $4$ cells of at least one of the two diagonals of the grid contain coins can be written as $\dfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.