Albert is situated on the coordinate plane at the point $(2,0)$. He wishes to give a textbook to his friend, who lives at $(0,1)$. Every step Albert takes, he moves one unit in either the positive $x$, positive $y$, negative $x$, or negative $y$ direction. How many paths of length $10$ can Albert walk such that he starts and ends at his home and he visits his friend’s house exactly once?