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 \(\frac{160}{729}\)
waec 2016furthermathematics

The correct answer is D. \(\frac{160}{729}\)

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

The coefficient of \(x^{3}\) is 

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

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

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