The number of onto functions (subjective functions) from set $$X = \left\{ {1,2,3,4} \right\}$$ to set $$Y = \left\{ {a,b,c} \right\}$$ is __________________.

Let $$X$$ and $$Y$$ denote the sets containing $$2$$ and $$20$$ distinct objects respectively and $$𝐹$$ denote the set of all possible functions defined from $$X$$ to $$Y$$. Let $$f$$ be randomly chosen from $$F.$$ The probability of $$f$$ being one-to-one is ________.

Consider the set of all functions $$f:\left\{ {0,\,1,.....,2014} \right\} \to \left\{ {0,\,1,.....,2014} \right\}$$ such that $$f\left( {f\left( i \right)} \right) = i,\,\,\,$$ for all $$0 \le i \le 2014.$$ Consider the following statements:
$$P$$. For each such function it must be the case that for every $$i$$, $$f\left( i \right) = i$$
$$Q$$. For each such function it must be the case that for some $$i$$, $$f\left( i \right) = 1$$
$$R$$. Each such function must be onto.

Which one of the following id CORRECT?

There are two elements $$x, y$$ in a group $$\left( {G,\, * } \right)$$ such that every elements in the group can be written as a product of some number of $$x's$$ and $$y's$$ in some order. It is known that
$$x * x = y * y = x * y * x * y = y * x * y * x = e$$
where $$e$$ is the identity element. The maximum number of elements in such a group is ______.