Generalized Sequential-Selection Formula for Structured Digit Permutations

This paper introduces a unified sequential-selection formula for calculating the total number of N-digit positive integers with specific structural digit frequencies (e.g., AABB, AAAB, AABBCC). By integrating sequential digit choices (9 × 9 × 8 ), multiset permutations, and a symmetry-reduction factor 1/k!, the proposed method simplifies counting across equal-frequency digit roles. This approach handles both multiset role symmetry and leading-zero exclusions in a single calculation, eliminating the need for extensive case analysis. Includes detailed derivations, worked examples, and a summary reference table.