If the coefficients of $\;x^{2}\;$ and $\;x^{3}\;$ in the expansion of $\;(1+ax+bx^{2}) (1-2x)^{18}\;$ in powers of x are both zero , then (a,b) is equal to :

Question

$(a)\;(14 , \large\frac{272}{3}) \qquad(b)\;(16 , \large\frac{272}{3})\qquad(c)\;(16 , \large\frac{251}{3})\qquad(d)\;(14 , \large\frac{251}{3})$