Question 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 $\dfrac{3}{5}$ of the green balls are on the same side of the red ball. Observe that $P(5)=1$ and that $P(N)$ approaches $\dfrac{4}{5}$ as $N$ grows large. What is the sum of the digits of the least value of $N$ such that $P(N)\lt\dfrac{321}{400}?$