For $$m, n > 0$$, let $$\alpha(m, n)=\int_\limits{0}^{2} t^{m}(1+3 t)^{n} d t$$. If $$11 \alpha(10,6)+18 \alpha(11,5)=p(14)^{6}$$, then $$p$$ is equal to ___________.

The number of ordered triplets of the truth values of $$p, q$$ and $$r$$ such that the truth value of the statement $$(p \vee q) \wedge(p \vee r) \Rightarrow(q \vee r)$$ is True, is equal to ___________.

Let $$S=109+\frac{108}{5}+\frac{107}{5^{2}}+\ldots .+\frac{2}{5^{107}}+\frac{1}{5^{108}}$$. Then the value of $$\left(16 S-(25)^{-54}\right)$$ is equal to ___________.

In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is _________.