Question

The coefficient of $t^4$ in the expansion of ${\left(\frac{1-t^6}{1-t}\right)}^3$ is

• A. 12
• B. 15
• C. 10
• D. 14

Answer 1

Answer: (B)

$(1-t^6{)}^3(1-t{)}^{-3}$
$(1-t^{18}-3t^6+3t^{12})(1-t{)}^{-3}$
$\Rightarrow$ cofficient of $t^4$ in $(1-t{)}^{-3}$ is
${}^{3+4-1}{C}_4={}^6{C}_2=15$