Solution: We compute the number of distinct permutations of a multiset with 13 total batches: 6 blue (B), 4 green (G), and 3 red (R). The number of sequences is:

Sat, 02 May 2026 23:02:23 +0000

Understanding the Number of Distinct Permutations of a Multiset: A Case Study with 6 Blue, 4 Green, and 3 Red Batches When dealing with sequences composed of repeated elements, calculating the number of distinct permutations becomes essential in fields like combinatorics, data science, and algorithm optimization. A classic example is determining how many unique sequences can be formed using multiset batches—such as 6 blue, 4 green, and 3 red batches—totaling 13 batches. ### The Problem: Counting Distinct Permutations of a Multiset Given a multiset with repeated items, the total number of distinct permutations is computed using the multinomial coefficient. For our case: