Pair It

You are given a set $X$ containing $N$ unique integers, $x_1, x_2, ..., x_n$, and a set $Y$ containing $N$ unique integers, $y_1, y_2, …, y_n$. Set $S$ is formed by pairing each element of set $X$ with an element of set $Y$, which has not been paired already, to form the set of points ($x_i$, $y_j$). Find the number of ways of forming set $S$ so that all the points in the set lie on a straight l