Place exactly one random walker at each integer in $\Bbb Z$ and define $Y_n$ as the number of these who are at the origin at time n. Show that $0<\displaystyle\lim_{n\to\infty}P\{Y_n=0\}<1$ and find $\displaystyle\lim_{n\to\infty}P\{Y_n=k\}$ for $k\in\Bbb Z^+$.
I'd like to get a hint to start, I don't know how to tackle this problem.