Why does order not matter when counting combinations?

In combinatorics, the distinction between permutations and combinations lies in whether the order of selection matters. A combination is defined specifically as a selection of objects from a set where order is not a factor.1

Order does not matter when counting combinations because the goal is to identify unique subsets rather than distinct sequences. In a permutation, the arrangement of items is considered significant; for example, selecting items A and B in that specific order (AB) is viewed as distinct from selecting them as BA.1

When counting combinations, however, these different arrangements are treated as a single, indistinguishable selection. Because any group of $k$ objects can be arranged in $k!$ different ways, there are $k!$ permutations for every unique combination. To account for this, the formula for combinations is derived by dividing the number of permutations by $k!$, effectively removing the influence of order from the final count.1