Write statements that will display a random number from each of the following sets: a) 2, 4, 6, 8, 10. b) 3, 5, 7, 9, 11. c) 6, 10, 14, 18, 22.

The concept of 'selection from a set' is foundational in programming when you need to pick an item randomly from a group of elements. A set, in this context, is any collection of distinct objects, typically represented in programming as an array, list, or any other data structure that can hold multiple values.

When faced with such a task, a programmer needs to ensure the selection is unbiased and truly random - all elements should have an equal chance of selection. To do this, most programming languages provide built-in functions or libraries that intelligently handle the complex algorithms required for random selection behind the scenes, abstracting these details from the developer.

This concept was applied to the original exercise by defining sets of numbers and employing a random choice function to select a number from each set, ensuring that each number had an equal probability of being displayed.

The random function is an indispensable tool in programming when you need to generate unpredictability or simulate real-life scenarios that involve chance. Various programming languages offer different libraries or modules to use random functions.

In Python, for instance, the 'random' module provides access to various functions such as 'random.choice()', which is used when one needs to randomly pick an element from a sequence such as a list. As shown in the step-by-step solution, 'random.choice([2, 4, 6, 8, 10])' randomly selects a number from the provided list of even numbers.

Utilizing such functions requires importing the necessary module first, then calling the appropriate method. Getting the syntax and method call correct is crucial to ensure the desired random behavior in your program.

Lists are vital data structures in programming. A list is an ordered collection of items which can be modified - items can be added, removed, or changed. Lists are flexible and easy to use, making them suitable for tasks that involve storing collections of items, such as sets of numbers to pick from randomly.

In the given exercise solutions, lists are used to store each set of numbers. Functions such as 'random.choice()' can then directly operate on these lists to select random elements. When working with lists, programmers must understand methods to manipulate them, such as appending elements, accessing via indices, slicing, and more.

It is also important to note that the efficiency of operations on lists can vary; for selecting a random item, however, efficiency is generally not a concern, as the operation is typically fast even for larger lists.