examday

/TMUA

Four distinct integers are chosen uniformly at random from $\{1,2,\ldots,12\}$. It is given that their sum is divisible by $3$.

Let $P$ be the monic polynomial of degree $4$ whose roots are the four chosen integers. What is the probability that both local minimum points of the graph $y=P(x)$ have $y$-coordinate $-9$?