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: Option D
Explanation
([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})