Find the coefficient of \(x^{3}\) in the expansion of \([\frac{1}{3}(2 + x)]^{6}\)

A.

\(\frac{135}{729}\)

B.

\(\frac{149}{729}\)

C.

\(\frac{152}{729}\)

D.

\(\frac{160}{729}\)

Correct answer is D

\([\frac{1}{3}(2 + x)]^{6} = (\frac{2}{3} + \frac{x}{3})^{6}\)

The coefficient of \(x^{3}\) is 

\(^{6}C_{3}(\frac{2}{3})^{3}(\frac{1}{3})^{3}x^{3} = (\frac{6!}{3!3!})(\frac{8}{27})(\frac{1}{27})x^{3}\)

= \(\frac{160}{729}\)