Let $\{X_n\}$ denote a symmetric random walk on the integers such that $X_n = \sum^n_{i=1} Y_i$ where $Y_i=\pm1$, each with probability $0.5$ and $X_0=0$.
Find $P(X_{10}=3)$. I know the formula for $P(X_n=0\mid X_0=0)$, but don't know how to apply it to other cases.