The coefficient of $$x^7$$ in $${(1 - x + 2{x^3})^{10}}$$ is ___________.

Let $$[t]$$ denote the greatest integer $$\leq t$$. If the constant term in the expansion of $$\left(3 x^{2}-\frac{1}{2 x^{5}}\right)^{7}$$ is $$\alpha$$, then $$[\alpha]$$ is equal to ___________.

The largest natural number $$n$$ such that $$3^{n}$$ divides $$66 !$$ is ___________.

The coefficient of $$x^{18}$$ in the expansion of $$\left(x^{4}-\frac{1}{x^{3}}\right)^{15}$$ is __________.