AMC 12 2016a Problem 13

Let $N$ be a positive multiple of $5$. One red ball and $N$ green balls are arranged in a line in random order. Let $P(N)$ be the probability that at least $\tfrac{3}{5}$ of the green balls are on the same side of the red ball. Observe that $P(5)=1$ and that $P(N)$ approaches $\tfrac{4}{5}$ as $N$ grows large. What is the sum of the digits of the least value of $N$ such that $P(N) < \tfrac{321}{400}$?

\textbf{(A)}\ 12 \textbf{(B)}\ 14 \textbf{(C)}\ 16 \textbf{(D)}\ 18 \textbf{(E)}\ 20