let $$G$$ be a group with $$15$$ elements. Let $$L$$ be a subgroup of $$G$$. It is known that $$L \ne G$$ and that the size of $$L$$ is at least $$4$$. The size of $$L$$ is ______.

Let $$\delta $$ denote the minimum degree of a vertex in a graph. For all planar graphs on $$n$$ vertices with $$\delta \ge 3$$, which one of the following is TRUE?

If $$G$$ is a forest with $$n$$ vertices and $$k$$ connected components, how many edges does $$G$$ have?

An operating system uses $$shortest$$ $$remaining$$ $$time$$ $$first$$ scheduling algorithm for pre-emptive scheduling of processes. Consider the following set of processes with their arrival times and $$CPU$$ burst times (in milliseconds):

Process	Arrival Time	Burst Time
P1	0	12
P2	2	4
P3	3	6
P4	8	5

The average waiting time (in milliseconds) of the processes is ________.