Suppose you want to go from bottom left to top right on an 8 by 8 rectangular grid. Which you were only allowed to move right or up direction. Let $P(X=k)$ where $k$ is the number of turns.
For example if the sequence is UUUUUUUURRRRRRRR there is only 1 turn
Question: given $k$, find $P(X=k)$ for any number of $k$
P.S. My friend told me to use stars and bars technique. But I did not get the reason behind that