MathDB

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}

N

grows large. What is the sum of the digits of the least value of

N

such that

P(N) < \tfrac{321}{400}

<span class='latex-bold'>(A) </span> 12 \qquad <span class='latex-bold'>(B) </span> 14 \qquad <span class='latex-bold'>(C) </span>16 \qquad <span class='latex-bold'>(D) </span> 18 \qquad <span class='latex-bold'>(E) </span> 20

Problem Statement