2016 AMC 12A 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\qquad\textbf{(B)}\ 14\qquad\textbf{(C)}\ 16\qquad\textbf{(D)}\ 18\qquad\textbf{(E)}\ 20

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.