The coefficient of $\mathrm{x}^{18}$ in the product $(1+x)(1-x)^{10}\left(1+x+x^{2}\right)^{9}$ is :
$-84$
84
126
-126
Correct Option: 1,
$(1+x)(1-x)^{10}\left(1+x+x^{2}\right)^{9}$
$\left(1-x^{2}\right)\left(1-x^{3}\right)^{9}$
${ }^{9} C_{6}=84$
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