The coefficient of the 7th term in the binomial expansion of \((2 - \frac{x}{3})^{10}\) in ascending powers of x is

A.

\(\frac{560}{243}\)

B.

\(\frac{841}{243}\)

C.

\(\frac{1120}{243}\)

D.

\(\frac{4481}{243}\)

Correct answer is C

\(^{10}C_{7 - 1} (2^{10 - 6}) (\frac{-1}{3})^{6}\)

\(\frac{10!}{(10 - 6)! 6!} \times 16 \times \frac{1}{243} \)

= \(210 \times 16 \times \frac{1}{729} \)

= \(\frac{1120}{243}\)