Find the coefficient of the \(6^{th}term\) in the binomial expansion of \((1 - \frac{2x}{3})10\) in ascending powers of \(x\).

A.

\(-\frac{896x^6}{9}\)

B.

\(-\frac{896x^5}{9}\)

C.

\(-\frac{896x^5}{27}\)

D.

\(-\frac{896x^6}{27}\)

Correct answer is C

rth term of a binomial expansion =\(^nC_r-1 a^{n-(r-1)}b^{r-1}\)

\(n = 10,r = 6 \therefore r-1=5\)

6th term =\(^{10}C_5 1^{10} - 5 (-\frac{2}{3}x)^5\)

\(=252*1*-\frac{32x^5}{243}=-\frac{896x^5}{27}\)