Question 17Integers $a$ 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 $x^3 + ax^2 + bx + 6$ has $3$ distinct integer roots?$\dfrac{1}{240}$$\dfrac{1}{221}$$\dfrac{1}{105}$$\dfrac{1}{84}$$\dfrac{1}{63}$