I have a questiontowhich I am struggling to come up with an answer. I have tried to solve it programmatically by recursion but I could not reach a satisfactory solution.

I would be glad if you share your ideas, thanks.

Q. n
married couples have to cross from the left to the right bank of a river via a narrow bridge, one by one. They decided that at any time on the left bank, the number of men should be no less than that of women; apart from this the order can be arbitrary. Find the probability that every man will cross the river after his own wife.