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A finite population is a set of distinct elements or items that can be counted. When working with populations in statistics, knowing whether it's finite or infinite helps in choosing the correct sampling methods.
In the exercise, the finite population consists of five distinct labels: A, B, C, D, and E. This small number makes it feasible to list all possible outcomes when choosing samples.
For finite populations, we can determine the exact sample space, in this case by listing every possible pair from the set. With a finite population, it is easier to apply statistical formulas, like the combination formula, to determine possibilities and probabilities.

The combination formula is useful for determining how many ways we can choose a subset from a larger set without considering the order of selection. This formula is especially helpful when dealing with finite populations.
The formula for combinations is expressed as \(\binom{n}{k}\), where \(n\) is the total number of elements in the population, and \(k\) is the number of elements we want in each sample. By applying this to our finite population of 5 elements and determining all combinations of 2, we calculate \(\binom{5}{2} = 10\).
This tells us there are 10 unique combinations of samples of size 2 that can be taken from this population. Importantly, this calculation confirms the process and provides the number needed to compute probabilities.

Probability measures how likely an event is to occur. In simple random sampling, every sample should have an equal chance of being selected.
In our exercise, we have 10 possible samples, each is equally likely to be selected. This is due to the nature of simple random sampling, which ensures each sample of the same size has the same probability.
The probability of selecting any one of these 10 samples is calculated as \(\frac{1}{10}\) or 0.1. So, each pairing of elements A to E as a group of two has this probability of being chosen in this method.