Question 12
Integers $a$ and $b$ are randomly chosen without replacement from the set of integers with absolute value not exceeding $10$. What is the probability that the polynomial $x^3 + a x^2 + b x + 6$ has $3$ distinct integer roots?
(A) $\frac{1}{240}$ (B) $\frac{1}{221}$ (C) $\frac{1}{105}$ (D) $\frac{1}{84}$ (E) $\frac{1}{63}$
(A) $\frac{1}{240}$ (B) $\frac{1}{221}$ (C) $\frac{1}{105}$ (D) $\frac{1}{84}$ (E) $\frac{1}{63}$