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  4. The coefficient of t4 in the expansion of ((1-t6/1-t))3 is

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

JEE MainJEE Main 2019Binomial Theorem

Solution:

$(1 - t^6)^3 (1 - t)^{-3}$
$(1 - t^{18} - 3t^{6} + 3t^{12}) (1 - t)^{-3}$
$\Rightarrow $ cofficient of $t^4$ in $(1 - t)^{-3}$ is
$^{3+4-1}C_4 = {^6C_2} = 15$