Why is the number of combinations smaller than the number of permutations for the same selection?

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combinatorics Figure 1: Ferrers' partitioning diagram for 14.

In combinatorics, the number of combinations is smaller than the number of permutations for the same selection because of how each method treats the order of objects.

A permutation considers the order of selection to be a factor, meaning that different arrangements of the same set of objects are counted as distinct outcomes. For example, if you select two letters from a set, "AB" and "BA" are counted as two separate permutations.1

In contrast, a combination focuses only on the membership of the subset, meaning the order of selection is not a factor. Consequently, "AB" and "BA" are considered the same subset. Because there are $k!$ possible arrangements for any selection of $k$ objects, each unique combination corresponds to $k!$ indistinguishable permutations. To find the number of combinations, you must divide the total number of permutations by $k!$ , which mathematically results in a smaller value.1