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At the heart of many mathematical and computer science problems lies the concept of combinations. It refers to the different ways you can group a certain number of items where the order does not matter. For example, if you have items labeled as 1, 2, and 3, the combinations of size 2 would be (1, 2), (1, 3), and (2, 3).

These groupings, such as (1, 2) and (2, 1), are considered identical in the world of combinations because they contain the same items, regardless of the order. It is a fundamental principle in the arenas of statistics, probability, and various branches of mathematics such as combinatorics. Understanding this concept is crucial when developing algorithms that need to handle data organization, selection processes, and decision-making scenarios.

Algorithm development is a step-by-step process aimed at solving problems or performing specific tasks. To develop an algorithm for the given exercise, one must firstly conceptualize what outputs are required. The output, in this case, is to list all possible combinations of a particular size from a set of objects.

Developing such an algorithm involves creating a method that systematically explores all potential groupings without repetition. This ensures efficiency and completeness. The approach generally starts with identifying the simplest possible case (often called a 'base case') and incrementally adding complexity to handle more advanced scenarios. Debugging and testing are integral to this phase to confirm the algorithm behaves as intended.

Translating the mathematical concept of combinations into practical programming requires using loops and conditional statements to mimic the selection process. For instance, creating selections of size 2 from a set of 6 objects involves iterating over each element and pairing it with all subsequent elements. This is achieved by using nested loops; the outer loop picks the first element, and the inner loop picks the second element of the pair.

In programming languages, this is usually accomplished using array or list structures and 'for' loops. For combinations of size 3, an additional layer of looping is required, where a third element is chosen as part of the existing pair. It is vital to ensure the indices do not overlap to avoid repetition of combinations. This demonstration of programming for combinations transfers a mathematical sequence into concrete, computational steps.

A pseudo algorithm is a simplified, informal description of the steps needed to solve a problem, and it’s written in a way that can be easily translated to actual computer code. For the exercise provided, a pseudo algorithm helps outline the logic without getting bogged down in the syntax of a specific programming language.

For part A, it can be expressed as follows:

1. Start a loop from index 1 to the end of the set (i).
2. Inside this, start another loop from index+1 to the end (j).
3. Output each pair (i, j).

For part B, the pseudo algorithm extends to:

1. Start a loop from index 1 to the end of the set (i).
2. Within loop (i), start another loop from index+1 to the end (j).
3. Within loop (j), start a third loop from index+1 to the end (k).
4. Output each trio (i, j, k).

This representative method provides clarity and a framework for actual code development, promoting a deeper understanding of the steps to the solution.